Oil prices mixed after Trump says no Iran deal needed: 'We've got their Strait'

Brent crude traded 1.1% higher at $93.73 per barrel. West Texas Intermediate futures were up just 0.3% at $86.76 per barrel.

Brent and WTI- YTD "We don't need a deal with Iran. Those days have long since passed. We've got their money, Hundreds of Billions of Dollars, and we've got their Strait!" Trump said in a Truth Social post .

Trump said Sunday that fresh attacks were highly unlikely as talks to end the conflict progressed, despite both ⁠countries reporting that shipping had been hit in or near the Strait of Hormuz. He also said further military action did not appear necessary "at this point," easing concerns about prolonged disruptions to Middle East oil supplies.

Trump's assertion that the U.S. controls the Strait of Hormuz could spur further Iranian attacks on shipping, increasing the risk of prolonged supply disruptions, according to Kilduff.

"In any event, it does not seem to me that either side's negotiating position has changed. Iran wants the blockade to end, sanctions to be lifted and a ceasefire including Lebanon to be declared. The USA wants Iran to get rid of its entire nuclear stockpile and allow free transit through the Strait of Hormuz," he said.

—CNBC's Pippa Stevens contributed to the report.