(Adds U.S. markets open, byline, dateline; previous LONDON)
* Wall St hits session high on Trump trade comments
* Dollar recovers after dropping on impeachment inquiry
* Oil falls as U.S. inventories rise
By Herbert Lash
NEW YORK, Sept 25 (Reuters) - The U.S. bucked weakness in other world stock markets and the dollar rebounded on Wednesday after President Donald Trump said a trade deal with China could happen sooner than expected.
A measure of global equity market performance fell and investors turned to safe-haven assets after House of Representatives Speaker Nancy Pelosi said on Tuesday the Democratic-led chamber was launching an official impeachment inquiry of Trump.
But European shares cut losses and U.S. stock indexes turned higher early in the session after Trump said a trade deal with China could happen sooner than expected.
Trump made the remarks to reporters a day after delivering a stinging rebuke to China's trade practices at the United Nations General Assembly, saying he would not accept a "bad deal" in U.S.-China trade negotiations.
Some market participants still expressed optimism in Wall Street's fortitude.
"As long as the economy remains firm, we don't think the drama out of Washington will impact the staying power of this bull market," said Ryan Detrick, senior market strategist at LPL Financial.
Euro zone bond yields rose and U.S. Treasury yields rebounded after seven straight sessions of losses on strong housing data and as investors took a cautious stance about Trump's possible impeachment.
A summary of a July phone call showed that Trump had asked Ukrainian President Volodymyr Zelenskiy to investigate his political rival, former vice president Joe Biden, and a company that employed Biden's son.
"The impeachment is not a big issue until you get into a recession. It's a big deal politically, but it's not a big deal economically," said Stan Shipley, fixed income strategist, at Evercore ISI in New York.
Sales of new U.S. single-family homes rebounded more than expected in August, the latest sign that the struggling housing market was starting to get a lift from lower mortgage rates.
The dollar also benefited from a sharp pullback for the pound amid worries that Brexit and general election related risks showed no signs of going away soon.
The dollar index rose 0.63%, with the euro down 0.59% to $1.0953. The Japanese yen weakened 0.63% versus the greenback at 107.76 per dollar.
On Wall Street, the Dow Jones Industrial Average rose 147.79 points, or 0.55%, to 26,955.56. The S&P 500 gained 7.38 points, or 0.25%, to 2,973.98 and the Nasdaq Composite added 19.81 points, or 0.25%, to 8,013.43.
The pan-European STOXX 600 index lost 0.70% and MSCI's gauge of stocks across the globe shed 0.23%.
Oil prices fell for a second day as U.S. crude inventories unexpectedly surged 2.4 million barrels in the week to Sept. 20, according to the Energy Information Administration, instead of declining 249,000 barrels as analysts expected.
Brent crude futures fell $1.14 to $61.96, a 1.8% drop. U.S. West Texas Intermediate crude fell 96 cents to $56.33 a barrel, a 1.6% loss.
Benchmark 10-year U.S. Treasury notes fell 17/32 in price to yield 1.6921%.
Reporting by Karin Strohecker, additional reporting by Saikat Chatterjee in London, Stanley White in Tokyo and Swati Pandey in Sydney; Editing by Bernadette Baum