By Herbert Lash

NEW YORK (Reuters) - The dollar rose and stocks on Wall Street lifted a gauge of global equities on Wednesday on robust U.S. housing data and the notion a strong economy would overcome any investor skittishness over a possible impeachment of President Donald Trump.

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."

Stocks in Europe were pressured by political uncertainty after Democrats in the U.S. House of Representatives moved to launch a formal impeachment inquiry of Trump.

But Wall Street shrugged off an impeachment investigation, with the benchmark S&P 500 posting its biggest daily gain in two weeks. Yields on U.S. Treasury long-dated debt rose after falling for seven straight sessions.

The White House released a summary of a telephone call between Trump and Ukraine's president, who said he was not pushed to investigate former Vice President Joe Biden, the front-runner for the 2020 Democratic presidential nomination.

"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.

MSCI's gauge of stocks across the globe rose 0.01%. The pan-European STOXX 600 index closed down 0.58% while in London, the FTSE 100 index fell 0.02%.

Michael Antonelli, market strategist at Robert W. Baird in Milwaukee, said good economic data is fighting with political noise and good data is winning.

Sales of new U.S. single-family homes rebounded more than expected in August, the latest sign that lower mortgage rates were starting to boost the struggling housing market.

"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.

The Dow Jones Industrial Average rose 162.94 points, or 0.61%, to 26,970.71. The S&P 500 gained 18.25 points, or 0.62%, to 2,984.85 and the Nasdaq Composite added 83.76 points, or 1.05%, to 8,077.38.

The dollar benefited from a sharp pullback for the pound amid worries about nagging Brexit- and election-related risks.

The dollar index rose 0.71%, with the euro down 0.69% to $1.0942. The Japanese yen weakened 0.67% versus the greenback at 107.81 per dollar.