SINGAPORE, April 1 (Reuters) - Stocks and bonds rallied and the dollar wallowed at the start of the Asian trading session on Wednesday on hopes of a de-escalation in the Iran conflict, while significantly better-than-expected economic data for March propelled a rebound in Korean and Japanese shares.

MSCI's broadest index of Asia-Pacific shares outside Japan was up 2.7%, snapping a four-day losing streak as South Korea's Kospi surged as much as 5.5%. The Nikkei 225 also jumped 3.9% at one point, after U.S. President Donald Trump said the United States could end its military attacks on Iran within two to three weeks and that Tehran did not have to make a deal as a prerequisite for the conflict winding down.

"They're still quite far apart in terms of what a truce means, or what peace means, but the market is embracing the fact that they are talking," said Rodrigo Catril, currency strategist at National Australia Bank in Sydney. 

"That's a positive sign, at least in terms of signalling or willingness to end the conflict," he said, speaking on a podcast. "Whether a compromise can be reached remains to be seen," he added. "While this is all happening, attacks are continuing from both sides."

Trump will provide an update on Iran in an address to the nation at 9 p.m. on Wednesday (0100 GMT on Thursday), White House spokeswoman Karoline Leavitt said on X. S&P 500 e-mini futures were up 0.3% and Nasdaq futures gained 0.5% after the post.

Stocks on Wall Street soared on Tuesday as traders bet on the potential off-ramp to the war, sending the S&P 500 2.9% higher, though oil markets were more subdued as trading resumed in Asia. Brent crude futures moved 1.1% higher to $105.16 a barrel to retrace some of the previous day's decline. 

South Korean stocks were on track for their sharpest jump in two weeks, with Samsung Electronics soaring 8% and SK Hynix up 7.8%, as exports soared 48.3% year-on-year in March, smashing market expectations, while a separate purchasing managers' index (PMI) gauge showed the country's factory activity expanded at the strongest pace in more than four years in March, led by semiconductor demand and new product launches.

In Japan, business sentiment among large manufacturers improved in the three months to March, according to a closely watched survey released on Wednesday, a sign that increasing economic uncertainty from the Middle East conflict has yet to hit morale. 

The U.S. dollar index, which measures the greenback's strength against a basket of six currencies, nudged up 0.1% to 99.8070 after logging its biggest one-day drop since March 19 on Tuesday, as traders reassessed the odds that the Federal Reserve may take policy action earlier than thought, rather than sitting on its hands all year.

Fed funds futures are pricing an implied 32% probability that a 25-basis-point cut to interest rates could come at the U.S. central bank's two-day meeting ending on July 29, compared to a 7.5% chance a day earlier, according to the CME Group's FedWatch tool.

The yield on the U.S. 10-year Treasury bond was down 1.2 basis points at 4.297%.

In cryptocurrencies, bitcoin was down 0.3% at $67,988.87, while ether slipped 0.2% to $2,100.94.