* Greenback recovers after Trump says he wants 'strong dollar'
* Oil up on tight supply and weak dollar, Brent passes $71
* Wall St surrenders gains after Trump talks up dollar (Updates with reaction to Trump comments on dollar)
By Caroline Valetkevitch
NEW YORK, Jan 25 (Reuters) - The dollar reversed losses and U.S. stocks relinquished gains after U.S. President Donald Trump backed a strong dollar.
The U.S. dollar index was last up 0.17 percent against a basket of major currencies after Trump told CNBC in an interview in Davos, Switzerland, that he wants to see a strong dollar.
The comments came a day after U.S. Treasury Secretary Steven Mnuchin, also in Davos, made a major departure from traditional U.S. currency policy, saying "obviously, a weaker dollar is good for us as it relates to trade and opportunities."
Mnuchin's comments drove further losses in the dollar on Wednesday, putting it at three-year lows.
"They want to walk back the yesterday's comments. They were salt in the wound," said Kathy Lien, managing director at BK Asset Management in New York.
But other factors have been driving the extended decline in the dollar, she said. "I think we are due for a rebound. What we are seeing now is some profit-taking."
The S&P 500 and Nasdaq were trading flat to down slightly, while the Dow was moderately higher.
The Dow Jones Industrial Average rose 105.07 points, or 0.4 percent, to 26,357.19, the S&P 500 lost 0.89 points, or 0.03 percent, to 2,836.65 and the Nasdaq Composite dropped 11.09 points, or 0.15 percent, to 7,403.97.
The pan-European FTSEurofirst 300 index lost 0.60 percent and MSCI's gauge of stocks across the globe shed 0.23 percent.
The euro was down 0.08 percent to $1.2396. Earlier, the euro rose to its highest in three years after the European Central Bank showed little concern about the single currency's hottest run in nearly four years.
The ECB kept its ultra-easy monetary policy unchanged. ECB President Mario Draghi cited the region's "solid and broad" growth and said inflation was likely to rise in the medium term.
U.S. benchmark 10-year notes last rose 9/32 in price to yield 2.6207 percent, from 2.654 percent late Wednesday.
U.S. crude slipped 10 cents to settle at $65.51 a barrel, while Brent fell 11 cents to settle at $70.42. Brent earlier hit $71 a barrel.
Additional reporting by Marc Jones in London and Richard Leong and Saqib Iqbal Ahmed in New York; Editing by Bernadette Baum and Nick Zieminski