By Auzinea Bacon, David Goldman, Hanna Ziady, CNN

(CNN) — Oil prices sank Monday, hitting their lowest levels in more than three months, after the United States and Iran said they had reached an agreement that would end a US blockade of Iranian ports and reopen the vital Strait of Hormuz.

Brent crude, the global oil benchmark, fell 5% to $82.91 a barrel shortly after 5 a.m. ET, having settled Friday at its lowest level since March 5, the first week of US-Israeli airstrikes against Iran. US crude dropped 5.5% to $80.21,also its lowest since early March. Both have fallen around $10 a barrel over the past week.

However, crude prices remainaround $10 a barrel higher than they were before the United States and Israel launched attacks on Iran in late February – and it could take many months for them to return to pre-war levels.

“Sentiment has clearly improved… but sentiment is not the same as supply,” Rystad Energy’s chief economist Claudio Galimberti wrote in a note Monday.

Markets have cheered apparent progress, but the oil market still has significant work ahead to return the flow of crude to normal. The Strait of Hormuz needs to be de-mined, ships need to be able to freely flow in and out of the strait, Middle East production needs to come back online, emergency petroleum reserves need to be refilled, and damaged energy facilities need to be repaired.

Oil analysts widely believe oil prices will remain elevated for quite some time. Even though prices may fall initially, they’re widely expected to bounce back once demand rises again — and particularly when emergency stockpiles get refilled.

Trump posted late Sunday afternoon on social media that a deal with Iran “is now complete.” The full text of the agreement has not yet been published, but the memorandum is expected to be signed Friday in Switzerland.

Both Trump and Iran’s deputy foreign minister for legal and international affairs signaled that the US blockade of Iran’s ports will be removed. Trump also said mines will need to be removed from the Strait of Hormuz, a crucial waterway for global oil supply.

Trump added that he authorized “the toll free opening of the Strait of Hormuz.” Ships have been charged about $2 million on average for passage, according to a member of Iran’s parliament.

The US and Iran have conflicting messages on what comes next after the agreement is signed. Iran’s deputy foreign minister said 60-day nuclear negotiations will begin only once the US releases billions in frozen funds. A US official rejected Iran’s assertions.

Even once the Strait of Hormuz is reopened, it will take time for oil flows to resume. Middle Eastern oil wells were largely shut off during the war and could take weeks to ramp up production when turned back on. Experts also warn that the wells may not return to pre-war production levels, due to the technical disruptions caused by prolonged shutdowns.

Oil prices could rebound if the disruption is prolonged and shock absorbers, such as the US Strategic Petroleum Reserve, are depleted, Bob McNally, president of Rapidan Energy, said Sunday on ABC’s “This Week.”

“I’m very concerned we could see oil prices skyrocket later this summer with crude oil prices heading well into the mid- to high-$100 range, and gasoline pump prices heading back to all-time highs around $5 a gallon,” he said.

And traders could remain skeptical that the strait has re-opened until ships start to transit regularly and safely.

“It’s great if it happens but I’ll believe it when I see actual ships making the free and unhindered passage through the strait,” said Joe McMonigle, president of think tank Global Center for Energy Analysis and who lives in Saudi Arabia.

The average price of gas in the US settled at $4.07 a gallon on Sunday, according to AAA. Gas prices have declined for three straight weeks, but are still about 36.6% higher than before the war began.

Stock futures, meanwhile, climbed. Dow futures gained 0.84%, while S&P 500 and Nasdaq futures were up 1.2% and 1.9% respectively. Stock markets in Asia and Europe also rallied.

“The fizz (is) staying in markets this morning as after 107 days and a seemingly endless number of false dawns, we finally have a deal between the US and Iran to end the war and open the Strait of Hormuz,” Deutsche Bank analysts wrote in a note.

They cautioned, however, that “tough conversations” are likely to follow the initial agreement to “ensure the peace is sustainable.”

CNN’s Matt Egan contributed reporting.