By Sophie Tanno, Daria Tarasova-Markina, and Lex Harvey, CNN

(CNN) — US President Donald Trump has said that Ukraine and Russia have agreed to stop hitting each other’s energy targets amid concerns over the global spike in fuel prices – but both his Ukrainian counterpart Volodymyr Zelensky and the Kremlin later described it as a proposal rather than a firm agreement.

Ukraine has been pummeling Russian fuel infrastructure for months, severely reducing Moscow’s refining capacity and triggering widespread supply shortages. In response, Russia, the world’s second largest diesel exporter behind the US, has banned the foreign sale of its diesel.

“There is now a strong US proposal for a mutual halt to strikes on critical infrastructure,” Zelensky said on Monday night. “If this can become the first de-escalatory step – a step toward ending Russian strikes on our critical infrastructure and our strikes in response – then Ukraine is ready to support de-escalation.”

Earlier on Monday, Zelensky alluded that the proposal would require help from Ukraine’s allies, saying in a social media post: “If our partners are ready to ensure that Russia genuinely refrains from striking our electricity system, other energy facilities, critical infrastructure, and food supply routes, then, of course, we are ready to ensure a corresponding halt to our strikes.”

Zelensky added the caveats that any agreement must be “reliable, long-term,” and “not fall apart after the Russians hold their ‘elections’ and get an easing of pressure on gasoline and diesel precisely for that period.”

His comments came after Trump on Monday claimed in a social media post that “Ukraine has agreed not to hit Russian Energy targets. Russia has agreed to do, likewise!”

Kremlin spokesperson Dmitry Peskov on Tuesday welcomed the proposal, calling it “a very good idea,” but did not confirm any agreement, saying instead that Russia was in contact with the American side and “will continue that dialogue.”

On Tuesday morning, Russia struck two gas stations on busy streets in Kyiv, officials said, while Zelensky said Ukrainians hit a refinery in Syzran, in Russia’s Samara region.

Trump has repeatedly voiced concerns that Kyiv’s attacks on diesel fuel sites in Russia were causing a shortage, as the war in Iran continues to spike global oil prices.

Diesel, a crucial fuel that powers trucks, trains, tractors and boats, topped $6 a gallon in the US on Friday for the first time ever, according to AAA, as global oil prices surpassed $108 per barrel amid the war in the Middle East.

Supplies have also been constricted by conflict in the Strait of Hormuz, which previously carried about one-fifth of the world’s oil supply, as the US and Iran battle for control of the vital waterway. Meanwhile, Saudi Arabia’s East-West pipeline, the oil-rich kingdom’s key alternative route to export its oil via the Red Sea was halted on Friday, after an attack by drones launched from Iraq, further complicating matters.

But Trump said the rise in diesel prices wasn’t “done by the Middle East,” instead attributing it to “what’s happening in Russia and Ukraine.”

Peskov said however that halting attacks on energy infrastructure would not address global supply issues, calling for the lifting of sanctions on Russian energy exports and “unhindered access for these petroleum products to global markets.”

In August, Moscow exported about 150,000 barrels of diesel per day, 81% below its five-year average as the export ban took effect, according to Vortexa.

Ukraine, which has also had its energy infrastructure repeatedly targeted by Russia, claims refineries are a legitimate target to cut off funding to Moscow and reduce domestic support for the war.

The Kremlin’s spokesman Dmitry Peskov said before Trump’s Monday post that the deteriorating situation for fuel markets is “primarily due to instability and fresh rounds of escalation in the Persian Gulf region.” He declined to comment on whether Russia would halt strikes on Ukraine’s economic and energy infrastructure.

Diesel prices reach new heights

Diesel costs have risen more than 55% since the start of the war with Iran, outpacing the 40% jump in gasoline prices. In fact, diesel is on track for its biggest annual percentage increase on record, according to a CNN review of AAA data.

While the price increase may be less visible to drivers, higher diesel prices tend to result in rising costs for businesses which are then offloaded to the consumer.

Beyond the skyrocketing cost of crude, part of the reason for the rising price of diesel is that refineries in the Middle East and Russia responsible for turning crude into fuel have been damaged in the wars.

“Refiners have already been maximizing the production of diesel. We simply can’t get any more diesel out of the system,” said Andy Lipow, president of Lipow Oil Associates, told CNN last week.

China’s export restrictions have also contributed to rising prices.

Ukraine has hit Russian oil facilities more than 300 times since the war began in 2022, severely disrupting supply across the country and forcing gas stations to ration supply, according to a CNN analysis from July.

Hours before Trump’s remarks, Ukraine’s military said it had struck an oil refinery in Russia’s Tatarstan republic overnight into Sunday.

The military said it struck the TANECO refinery in the city of Nizhnekamsk, in an attack carried out alongside the Security Service of Ukraine and the Main Intelligence Directorate.

Tatarstan officials said two civilians were killed and others wounded in the Ukrainian attack.

CORRECTION: This story has been updated to correct the attribution of the strikes in Russia’s Samara region.