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.

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Stock markets were mixed, with MSCI's broadest index of Asia-Pacific shares outside Japan advancing 0.8 percent, while Japan's Nikkei shed 0.2 percent.

Nasdaq futures trimmed earlier gains to trade 0.9 percent higher, while S&P 500 futures rose 0.68 percent.

EUROSTOXX 50 futures eased 0.36 percent, while FTSE futures added 0.4 percent and DAX futures lost 0.43 percent.

"The market wants to believe that it's all going to end soon, because the war not ending is quite bad for the world economy. The world economy's had these buffers of running down inventories, but you can't keep running down inventories," said Capurso.

Dollar steadies

In currencies, the dollar steadied on Tuesday on renewed safe-haven demand, though it remained some distance away from a six-week peak hit last week.

The euro fell 0.06 percent to $1.1636, while sterling eased to $1.3498.

Against the yen, the dollar was flat at 158.95.

Bonds were largely steady after a rout last week on worries that higher energy prices for longer would stoke a resurgence in inflation and prompt rate hikes across both developed and emerging markets.

The yield on the two-year US Treasury note was last little changed at 4.0612 percent, while the 10-year yield fell to 4.5024 percent.

"We are likely to see periodic yield retracements on occasions when geopolitical risks subside, but inflation and fiscal risks are likely to be more sustained," said Eric Robertsen, Standard Chartered's head of global research and chief strategist.

"Commodity supply dislocations will take months to resolve, and fiscal support measures are likely to drive a sustained deterioration in sovereign balance sheets — which will also require increased borrowing in an environment of higher funding costs."

Elsewhere, spot gold was down 0.5 percent at $4,545.90 an ounce.

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