The run-up in crude oil futures paused on Monday, with prices falling more than 1% on signs that Iran wants a ceasefire with Israel.

U.S. crude oil lost $1.21, or 1.66%, to close at $71.77 per barrel, while global benchmark Brent fell $1, or 1.35%, to settle at $73.23. Oil prices had rallied more than 7% Friday after Israel launched a wave of airstrikes against Iran's nuclear and ballistic missile programs as well as its military leadership.

The attacks continued for a fourth day Monday, with Israel claiming to have achieved "aerial superiority" over Iran, according to a military spokesperson.

Iran has asked Qatar, Saudi Arabia, Oman, Turkey and a few European countries to urge President Donald Trump to put pressure on Israel for a ceasefire, a Middle East diplomat with knowledge of the matter told NBC News. Tehran has promised flexibility on nuclear talks in exchange, the diplomat said.

Trump confirmed Monday that Iran had signaled through intermediaries that it wants to de-escalate the conflict.

"They'd like to talk, but they should have done that before," Trump told reporters during the G7 summit in Canada. "They should talk and they should talk immediately before it's too late."

U.S. crude oil prices touched an overnight high of $77.49 per barrel after Israel targeted two natural gas facilities in Iran. But prices later pulled back on optimism that the conflict hadn't yet had a material impact on global energy markets and the Persian Gulf and Strait of Hormuz remained open to shipping.

Despite the conflict, oil prices are unlikely to break above $80 per barrel, according to consulting firm Rystad Energy. The Trump administration wants oil prices closer to $50 per barrel and has an interest in containing the conflict to prevent energy prices from skyrocketing, Rystad said.

"We maintain our view that this is likely to remain a short-lived conflict, as further escalation risks spiraling beyond the control of key stakeholders," said Janiv Shah, vice president of commodities markets at Rystad.

Israel hits energy facilities

Other analysts cautioned against assuming that the conflict will be short. It could drag on for another couple weeks at least, said Helima Croft, global head of commodity strategy at RBC Capital Markets.

"The Israelis seem to be preparing for a longer conflict," Croft told CNBC's "Power Lunch" on Monday. A protracted conflict raises the possibility that oil export facilities and infrastructure in the region could be targeted, she said.

So far, Israel and Iran have only hit domestic energy infrastructure. Israeli drones struck the South Pars gas field in southern Iran on Saturday, according to Iranian state media reports. The strikes hit two natural gas processing facilities, state media said.

The extent of the damage to the facilities, one of the largest natural gas fields in the world, wasn't disclosed. Israel also hit a major oil depot near Tehran, sources told The Jerusalem Post.

Iranian missiles, meanwhile, damaged an oil refinery in Haifa, according to The Times of Israel.

Iran is considering shutting down the Strait of Hormuz, senior commander and parliament member Esmail Kowsari said Saturday. About one-fifth of the world's oil is transported through the strait on its way to global markets, according to Goldman Sachs. A closure of the strait could push oil prices above $100 per barrel, according to Goldman.

Iran would have a difficult time closing the strait due to the presence of the U.S. Fifth Fleet in Bahrain, Croft told CNBC's "Squawk Box" on Friday. "But they could target tankers there, they could mine the straits," she said.

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