* Weekly U.S. jobless claims fall unexpectedly, labor market solid

* U.S. trade deficit fell in February to lowest since Oct. 2009

* Friday’s U.S. nonfarm payrolls next key test for dollar

* ECB says it will “remain firm” on implementing QE program (Recasts, adds fresh comment, updates prices, changes byline)

By Gertrude Chavez-Dreyfuss

NEW YORK, April 2 (Reuters) – The dollar fell for a second straight session on Thursday, as investors continued to pare back hefty positions ahead of an all-important U.S. non-farm payrolls report that could disappoint those with a bullish view on the greenback.

A Reuters poll expects non-farm payrolls to rise by 245,000 jobs in March, after gaining 290,000 in February, but many in the market are bracing for a weak number. Economists at major banks though have not changed their forecast on jobs despite an underwhelming report on U.S. private sector employment released on Wednesday.

“This is just positioning ahead of payrolls and the fear is that payrolls could come in weaker than expected,” said Vassili Serebriakov, currency strategist, at BNP Paribas in New York.

Investors also took profits on recent greenback strength heading into the long Easter holiday weekend.

In late trading, the dollar index was down 0.7 percent at 97.485, with the greenback down 0.8 percent versus the Swiss franc at 0.9593.

Against the yen, the dollar was flat at 119.705.

Kathy Lien, managing director at BK Asset Management in New York said Friday’s non-farm payrolls report is especially important because the dollar has pulled back and investors are divided on when the Federal Reserve will raise rates.

“If the labor market report is strong, it will harden the case for a summer hike and revive the rally in the dollar,” Lien said. “However if job growth falls short of expectations, the dollar could extend its slide against most major currencies.”

The euro rallied more than 1 percent against the dollar, trading at $ 1.0886.

Even with the euro’s present rally, the rate differential between the United States and Europe is expected to grow as the European Central Bank maintains its money-printing quantitative easing policies.

Minutes from the ECB’s March 5 meeting showed monetary policymakers agreed to “remain firm” in implementing the QE program, even though the economic outlook is improving.

Markets in most of Europe will remain shut on Friday and Monday for Easter holidays. The U.S. bond market will have a shortened session while the U.S. stock market will be shut on Friday.

On Thursday, data showed the number of weekly applications for new employment benefits fell unexpectedly while February’s U.S. trade deficit narrowed to it lowest point since October 2009. However that still is unlikely to change views that U.S. economic growth slowed sharply in the first quarter.

(Reporting by Gertrude Chavez-Dreyfuss; Additional reporting by Daniel Bases; Editing by Diane Craft)