By Isabel Wang and Myra P. Saefong

Talks with Iran are 'continuing, at a rapid pace,' and Israel and Hezbollah have agreed to stop attacking each other in Lebanon, President Trump said in a post on Truth Social Monday afternoon

Oil prices were trimming earlier gains but staying sharply higher on the first trading day of June after President Donald Trump said U.S.-Iranian peace talks had resumed following a pause on Monday morning, when Iran reportedly suspended all exchange of negotiation messages with the U.S. due to continued Israeli cease-fire violations in Lebanon.

The West Texas Intermediate crude contract for July delivery (CL.1) (CLN26) was popping 5.2% to $91.90 a barrel after hitting a session high of $94.78 in morning action. Brent crude's August contract (BRN00) (BRNQ26) was up 4.1% to $94.98 a barrel, also coming off its session high, according to FactSet data.

The moves followed reports on Monday morning that Iranian negotiators would stop exchanging messages with the U.S. through intermediaries and that Tehran would move to fully close the Strait of Hormuz in retaliation for ongoing cease-fire violations, according to Iran's state-affiliated media outlet Tasnim.