By Nadeen Ebrahim, CNN

(CNN) — A second round of nuclear talks between the United States and Iran concluded on Saturday, with both sides indicating progress.

Delegations from both countries met in Rome for negotiations following an initial round in Oman last weekend. The Gulf Arab nation has mediated both rounds of the indirect talks, including an upcoming third high-level round expected in Oman on Saturday.

The Trump administration expressed optimism following the latest talks, pointing to “very good progress” and saying the parties had “agreed to meet again” next week. “Today, in Rome, over four hours in our second round of talks, we made very good progress in our direct and indirect discussions,” a senior administration official told CNN.

Iranian Foreign Minister Abbas Araghchi also signalled that the talks had been positive. “I can say that there is movement forward. We’ve reached better understanding and agreement on some principles and goals in these Rome negotiations,” he said.

President Donald Trump has threatened that the US will resort to military strikes against Iranian nuclear sites, with Israel’s help, should Tehran fail to reach a deal with its interlocutors.

Members of the Trump administration have flip-flopped in remarks over the past week, oscillating between maximalist demands that Iran has said were “red lines” and a more conciliatory approach.

Here’s what we know.

How the two sides got here

A nuclear deal was reached in 2015 between Iran and world powers, including the US. Under the deal, Iran had agreed to limit its nuclear program in exchange for the lifting of sanctions.

That agreement was, however, abandoned by Trump in 2018 during his first presidential term. Iran retaliated by resuming its nuclear activities and has so far advanced its program of uranium enrichment up to 60% purity, closer to the roughly 90% level that is weapons grade.

Iran insists its nuclear program is peaceful.

Last month, Trump sent a letter to Iran’s Supreme Leader Ayatollah Ali Khamenei proposing negotiations on a new nuclear deal, making it clear that Iran had a two-month deadline to reach an agreement, a source familiar with the letter’s contents told CNN.

Days later, Iranian President Masoud Pezeshkian said the Islamic Republic rejected direct negotiations with the US. He said however that Iran’s response, delivered by Oman, left open the possibility of indirect talks with Washington.

What does Trump want and what are the key issues?

Trump has said that the deal he seeks with Iran would not be similar to the 2015 agreement inked under the Obama administration.

“It’ll be different, and maybe a lot stronger,” he said.

Comments from Middle East envoy Steve Witkoff, who has represented the US in the talks, have suggested differently as of late.

Iran has in recent weeks been vocal with its concerns about striking a nuclear deal with Trump, who it says has a history of backtracking. The Islamic Republic has also voiced objections to any deal that fully dismantles its nuclear program, as opposed to limiting its uranium enrichment to civilian-only use – as was stipulated under the 2015 agreement.

Formally known as the Joint Comprehensive Plan of Action (JCPOA), the 2015 deal ensured through a number of mechanisms that Iran’s nuclear program would be exclusively peaceful.

Conflicting remarks from US officials before and after the first high-level meeting, on April 12,have muddied Washington’s demands.

Witkoff, who represented the US, said that moving forward, talks with Iran would be about verification of its nuclear program, but stopped short of mentioning a demand to fully dismantle Iran’s nuclear program, as other US officials have said in the past. In other words, indicating a deal that would be similar to the Obama-brokered agreement.

“The conversation with the Iranians will be much about two critical points,” Witkoff told Fox News on April 14. The first is verification of uranium enrichment, “and ultimately verification on weaponization, that includes missiles, type of missiles that they have stockpiled there, and it includes the trigger for a bomb.”

However, Witkoff reversed his position a day later in a statement on X in which he said any final deal with Iran would require it to “stop and eliminate its nuclear enrichment and weaponization program.”

Asked to explain Witkoff’s apparent reversal, an administration official told CNN: “It’s the most recent elaboration of policy.”

Other officials have been hawkish on what the US expects from Iran. A day after Witkoff started the largely indirect talks with Iranian negotiators in Oman, US Defense Secretary Pete Hegseth called on Tehran to fully dismantle its nuclear program.

“Iran, come to the table, negotiate, full dismantlement of your nuclear capabilities,” he said on Fox News.

Iranian officials have dismissed that proposal as a non-starter, accusing the US of using it as a pretext to weaken and ultimately topple the Islamic Republic. Tehran is entitled to a civilian nuclear energy program under a UN treaty.

The UN nuclear watchdog has however warned that Iran has been accelerating its enrichment of uranium up to alarming levels.

What is Iran saying?

In the week following the first high-level meeting, Iran doubled down on its right to enrich uranium and accused the Trump administration of sending mixed signals.

“Iran’s enrichment (program) is a real and genuine matter, and we are ready to build trust regarding potential concerns, but the issue of enrichment is non-negotiable,” Araghchi told reporters, state-run Press TV reported.

Foreign ministry spokesperson Esmaeil Baqaei weighed in on X, likening the shifting US position to “a professional foul and an unfair act in football.”

“In diplomacy any such shifting (pushed by hawks who fail to grasp the logic/art of commonsensical deal-making) could simply risk any overtures falling apart,” he wrote. “It could be perceived as lack of seriousness, let alone good faith… We’re still in testing mode.”

Iranian media has reported that Tehran had set strict terms ahead of the talks with the US, saying that “red lines” include “threatening language” by the Trump administration and “excessive demands regarding Iran’s nuclear program.” The US must also refrain from raising issues relating to Iran’s defense industry, Iranian media said, likely referring to Iran’s ballistic missile program, which the US’ Middle Eastern allies see as a threat to their security.

Meanwhile, Iran’s highest leadership has approached the talks with extreme caution. In his first comments on the issue, Khamenei said that Tehran was “neither overly optimistic nor overly pessimistic” about talks with the United States over its nuclear program.

What comes next?

The third round of high-level talks will be held next Saturday, according to Iran’s foreign ministry spokesperson. Oman’s foreign ministry confirmed that the meeting would take place in the capital, Muscat.

Omani Foreign Minister Badr bin Hamad Al Busaidi, who has been mediating the talks, called them “highly constructive” and said they were “gaining momentum.”

“Now even the unlikely is possible,” he wrote on X.

Iranian officials had said talks between technical experts would begin in Oman on Wednesday ahead of a third round of high-level talks on Saturday.

But US sources familiar with the talks said both political level and at the technical level talks will both take place on Saturday for now. The planning has been fluid, however, so it’s possible that the plan changes again, multiple sources said.

In the meantime, Iranian foreign minister Araghchi is due in Beijing this week for talks with Chinese officials.

Where does Israel stand?

Israel has been among the staunchest advocates for Iran to fully dismantle its nuclearprogram so it can never acquire a nuclear bomb.

Sources familiar with the matter had previously told CNN that news of the US-Iran nuclear talks were “certainly not” to Israel’s liking, and it remains unclear if Netanyahu was given advance notice of the negotiations or if he was consulted ahead of time, the sources said.

Netanyahu has touted a Libya-style nuclear deal between the US and Iran, which in 2003 dismantled the North African nation’s nuclear program in the hopes of ushering in a new era of relations with the US after its two-decade oil embargo on Moammar Gadhafi’s regime.

After relinquishing its nuclear program, Libya descended into civil war following a 2011 NATO-backed uprising that toppled Gadhafi’s regime and led to his killing. Iranian officials have long warned that a similar deal would be rejected from the outset.

Dermer and Mossad director David Barnea met Friday with Witkoff in Paris ahead of the second round of Iran talks.

Earlier this year, US intelligence agencies warned both the Biden and Trump administrations that Israel would likely attempt to strike facilities key to Iran’s nuclear program this year, according to sources familiar with the assessments.

However, The New York Times reported Wednesday that Trump had waved Israel off striking Iran’s nuclear sites as soon as next month to let talks with Iran play out. The Israeli Prime Minister’s Office did not deny the veracity of the article, instead asserting that Israel’s actions have delayed Iran’s nuclear program.

Responding to the New York Times’ report, Trump said Thursday: “I wouldn’t say waved off,” but “I’m not in a rush to do it because I think that Iran has a chance to have a great country and to live happily without death.”

He added: “I hope they (Iran) want to talk, it’s going to be very good for them if they do, and I’d like to see Iran thrive in the future, do fantastically well.”

What do Iran’s Arab neighbors think?

Unlike in 2015, when Gulf Arab states privately fumed over a deal they had publicly endorsed, Iran’s neighbors are now more supportive of its efforts to reach a new agreement with the US.

This time, they’re playing a more active role, with Iran keeping them in the loop on the talks’ progress. The Iranian foreign minister has spoken with his counterparts in several Arab capitals to brief them on the negotiations.

The United Arab Emirates was a key messenger before talks began, sending a letter on behalf of the Trump administration that urged Iran to start negotiations.

Saudi Arabia, whose oil infrastructure was once targeted by Iranian-backed militias, has offered to mediate between the Trump administration and Tehran in pursuit of a new deal, CNN previously reported.

Saudi Defense Minister Prince Khalid bin Salman Al Saud visited Tehran on Thursday in a rare trip by a senior Saudi royal to the Islamic Republic. Iran’s ambassador to Saudi Arabia, Alireza Enayati, said in an interview with Al Arabiya on Monday that the visit marked a “turning point” in relations.

“We entered a new era of relations with the visit of the Saudi defense minister,” Enayati said, adding that the future of Iranian-Saudi ties is promising.

Prince Khalid even met with Supreme Leader Ayatollah Ali Khamenei, who said that Iran is “fully prepared” to overcome the hostile intentions of those who oppose enhanced ties between the two countries.