* Greenback recovers after Trump says he wants 'strong dollar'
* Oil ends lower as dollar rebounds
* Dow, S&P 500 hit record closes but relinquished bigger gains (Updates to U.S. markets close)
NEW YORK, Jan 25 (Reuters) - The U.S. dollar edged up on Thursday, reversing its recent decline, after U.S. President Donald Trump backed a strong dollar, and the S&P 500 gave back gains on the comments before eking out a record-high close.
The U.S. dollar was up 0.17 percent against a basket of major currencies after Trump told CNBC in an interview in Davos, Switzerland, 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, which gave the currency its biggest daily percentage drop in seven months.
"They want to walk back 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 Dow and S&P 500 closed at their highest levels ever although they relinquished bigger gains after Trump's comments.
The Dow Jones Industrial Average rose 140.67 points, or 0.54 percent, to end at 26,392.79, the S&P 500 gained 1.71 points, or 0.06 percent, to 2,839.25 and the Nasdaq Composite dropped 3.90 points, or 0.05 percent, to 7,411.16.
The pan-European FTSEurofirst 300 index lost 0.60 percent and MSCI's gauge of stocks across the globe gained 0.13 percent.
The euro was down 0.09 percent to $1.2395. Earlier, the euro rose to its highest in three years after the European Central Bank showed little concern about the euro zone 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. Treasury debt prices rose, boosted by solid demand for 7-year notes as well as Trump's remarks on the dollar.
U.S. benchmark 10-year notes last rose 9/32 in price to yield 2.6207 percent, from 2.654 percent late Wednesday.
Oil retreated as the U.S. dollar rebounded from early losses and strengthened, denting support for the latest crude rally.
Brent crude, the international oil benchmark, settled down 11 cents at $70.42 a barrel. U.S. crude futures for March delivery fell 10 cents to settle at $65.51.
(Additional reporting by Marc Jones in London and Richard Leong and Saqib Iqbal Ahmed in New York; Editing by Nick Zieminski and James Dalgleish)