An unexpected fall in German industrial output for the third straight month helped to weaken the euro. The drop was modest, but it underscored concerns about a slowdown and the European Central Bank's caution as it tries to wean the region off stimulus.

German exporters are struggling with weaker global demand and trade disputes driven by U.S. President Donald Trump's policies.

In afternoon trading, the euro fell 0.3 percent to $1.1441. It has traded in a tight range of $1.12 to $1.15 since mid-November.

Weakness in the euro supported the dollar, which rose 0.3 percent against a basket of currencies to 95.908 <.DXY>.

The dollar index, however, has lost around 2 percent since mid-December and remains near a three-month low of 95.638 reached on Monday.

Despite Tuesday's rebound, the dollar's outlook remained dreary.

Federal Reserve Chairman Jerome Powell said on Friday the Fed is not on a preset path of rate hikes and will be sensitive to the downside risks markets are pricing in.

The prospect of no further rate increases is likely to keep the dollar under pressure, analysts said.

Mark McCormick, TD Securities North American head of FX strategy in Toronto, said his company's growth signals are still modestly long U.S. dollars, although the extreme overvaluation of as much as 20 percent on some models could offset that.

Overall, McCormick is leaning more U.S. dollar-bearish.

"The prospects of growing fiscal support outside the U.S. should amplify the growth convergence story this year just as the Fed nears the endgame and temporary U.S. support ebbs," said McCormick.

That said, dollar sentiment has been temporarily bolstered by optimism about a possible U.S.-China trade agreement.

U.S. Commerce Secretary Wilbur Ross said on Monday there was a good chance Beijing and Washington would reach a trade deal that "we could live with."

Against the yen, the dollar was little changed at 108.63 yen.

The British pound traded down 0.5 percent at $1.2716 and traders expect the currency to remain volatile over the next few weeks.

British Prime Minister Theresa May must win a vote in Parliament next week to approve her government's Brexit agreement or risk seeing Britain's exit from the European Union descend into chaos.

(Reporting by Gertrude Chavez-Dreyfuss; Editing by Dan Grebler and James Dalgleish)

By Gertrude Chavez-Dreyfuss