Oil rose early Monday, as traders continue to assess mixed signals from the U.S. and Iran amid worries that a deal between both countries to open the Strait of Hormuz may not be anytime soon.

Futures for international benchmark Brent crude for October delivery gained 1.09% to $84.46 a barrel. U.S. West Texas Intermediate futures for September advanced 0.84% to $78.84 per barrel.

Iranian Foreign Minister Abbas Araghchi said that Tehran is not currently in direct talks with the U.S. to end the war with Iran and open the Strait of Hormuz, while Washington earlier asserted that a deal is near.

In addition, Iran has asked the U.S. for compensation as a condition to reopen the crucial waterway, according to a report by media outlet Independent. The Strait of Hormuz will remain shut until the U.S. meets six conditions, including ending the war and aggression against Iran and its allies, Mohammad Bagher Zolghadr, the head of Iran's supreme national security council, reportedly said.

However, the U.S. maintains that any reopening must preserve unrestricted freedom of navigation without Iranian approvals, tolls, or controls, disputing key elements of the reported arranged, according to Citi. "Risks remain elevated outside Hormuz too, with Houthi groups in Yemen continuing attacks and threats against Saudi-linked shipping in the Red Sea and around Bab el Mandeb," it added.

"Uncertainty remains high as we go into the sixth month of the Iran war," Westpac said in a note. "The Strait of Hormuz remains effectively closed and the entry of the Yemen Houthis into the fray is interrupting alternative Red Sea supply routes," it added.

*—CNBC's Garrett Downs contributed to the report. *