TREASURIES-Yields fall as Iran submits fresh proposal for US talks

(Updated in New York afternoon)

* Trump rejects Iran's latest proposal, Iran open to talks if US changes stance

* Fed signals less easing bias, some officials warn of possible rate hikes amid oil shock

* Market focus shifts to April jobs data and Treasury's updated funding estimates

By Karen Brettell

NEW YORK, May 1 (Reuters) - U.S. Treasury yields fell on Friday alongside oil prices as traders weighed prospects for a deal to end the Iran war. U.S. President Donald Trump said he was not satisfied with the latest Iranian proposal for talks, while Iran's foreign minister said Tehran was ready for diplomacy if the United States changes its approach.

Yields have risen over the past two weeks on concerns that ongoing energy disruptions will keep oil prices elevated and fuel a renewed increase in inflation, which is already running above the Federal Reserve's 2% annual target.

Developments in the Middle East have contributed to high uncertainty about the economic outlook, overshadowing other market factors despite generally improving U.S. economic data.

"The market is less responsive to economic data in a backdrop that's been so battered by the back and forth of the geopolitical headlines," said Jonathan Cohn, head of U.S. rates desk strategy at Nomura.

The market also weakened on Wednesday after the Federal Reserve's meeting produced a more hawkish outcome than expected. The Fed left its benchmark overnight interest rate unchanged, as expected, but three members dissented over language suggesting the central bank could eventually resume rate cuts.

"The easing bias on the Fed is weaker, with more Fed participants pushing for symmetric language," said Cohn. "From the market's perspective, I don't necessarily see a clear read-through given we have already had a very meaningful repricing of policy expectations. Right now, markets are expecting very little over the next year."

Fed funds futures show that markets expect the U.S. central bank to stay on hold for the near term, though the probability of a hike increased early next year. Fed officials who dissented against this week's policy statement said on Friday the oil price shock from the war with Iran means the U.S. central bank should be clear it can no longer lean toward interest rate cuts, with a rise in borrowing costs possible. Trump also said on Friday he would increase tariffs on cars and trucks from the European Union to 25% next week, saying the bloc had not complied with its trade deal with Washington.

The 2-year note yield, which typically moves in step with Fed interest rate expectations, fell 0.1 basis points to 3.884%. The yield on benchmark U.S. 10-year notes fell 1.6 basis points to 4.374%.

The yield curve between 2- and 10-year notes flattened by around a basis point to 49 basis points.

Jobs data will be the main economic focus next week, culminating in Friday's payrolls report for April. Employers are expected to have added 60,000 jobs during the month, according to the median estimate of economists polled by Reuters.

The U.S. Treasury will also provide its updated funding estimates for the coming two quarters.

"I think a question that will be debated going into next week is whether or not Treasury decides to amend its forward guidance regarding no changes for at least the next several quarters," Cohn said. The Treasury repeated the guidance at its last update in February.

(Reporting by Karen Brettell; Editing by Nia Williams, Rod Nickel)