Trump's announcement briefly pared the dollar's losses, but traders said the currency reaction was not as strong as expected.

The agreement called for three weeks of stop-gap funding and a senior Democratic aide said the money the president demanded for a border wall is not included. Trump had previously insisted on the inclusion of $5.7 billion to help pay for a wall along the vast U.S.-Mexico border in any legislation to fund government agencies.

"The dollar's reaction has not been super strong because the uncertainty remains," said Juan Perez, senior currency trader, at Tempus Inc in Washington

"And it's also a temporary reopening. He was also actually adamant that a permanent solution should be made," Perez added.

The shutdown dragged on for 35 days, affecting 800,000 furloughed workers. In one of the many effects of the shutdown, hundreds of flights have been cancelled or delayed at airports in the New York area and Philadelphia.

In afternoon trading, the dollar index was down 0.8 percent at 95.812, earlier falling to a one-week low. On Thursday, the dollar climbed to a three-week high of 96.676.

Paul Ashworth, chief U.S. economist, at Capital Economics in Toronto, said Trump caved "presumably ... because of the damage the shutdown is having on his own approval ratings, particularly now that the shutdown is beginning to have a wider impact."

The dollar has been on the defensive all day as traders' focus shifted to the Federal Reserve's policy meeting next week when the U.S. central bank is expected to leave interest rates unchanged after raising them four times last year.

The euro, on the other hand, rebounded on Friday, steadying after a dovish European Central Bank president failed to alter an already downbeat assessment on the euro zone's economy.

The single currency rose 0.9 percent to $1.1412.

ECB President Mario Draghi warned on Thursday a dip in the euro zone's economy could be more pronounced than thought a few weeks ago, comments seen as signalling a delay in the bank's first interest rate hike.

The euro on Thursday weakened broadly on those comments and fell to a two-month low of $1.1286.

Sterling, meanwhile, hit a more than three-month high against the dollar after a report in the Sun newspaper that Northern Ireland's Democratic Unionist Party had privately decided to offer conditional backing for British Prime Minister Theresa May's Brexit deal next week.

(Reporting by Gertrude Chavez-Dreyfuss; Editing by Paul Simao and Grant McCool)

By Gertrude Chavez-Dreyfuss