Oil prices rose on Tuesday and stocks were mixed as investor optimism over an imminent US–Iran peace deal was tempered by new US strikes in the Middle East.Iran's top negotiator and its foreign minister were in Doha for talks with Qatar's prime minister on a potential deal with the US to end the war, an official briefed on the visit said, after Washington and Tehran played down hopes for an imminent breakthrough.

The Nikkei newspaper separately reported that both parties were discussing a plan to open the Strait of Hormuz about 30 days after reaching a deal to end hostilities.

But even as the talks proceeded, US forces conducted strikes on Monday in southern Iran against targets including boats attempting to lay mines and missile launch sites, in what they described as defensive actions.

The developments sent Brent futures rising more than 1 percent in early Asian trade to $97.32 a barrel. US West Texas Intermediate crude was up slightly from Monday's last traded price but down 5.5 percent from Friday's close. There was no settlement on Monday due to the US Memorial Day holiday.

"I'm a bit sceptical [...] We keep being told there's a deal that's near, but what does the deal look like? That's what's really important. When's the Strait of Hormuz going to open [...] There's a lot we don't know," said Joseph Capurso, a strategist at Commonwealth Bank of Australia.