* Dollar bounce after Fed meeting short-lived
* Greenback pares gains against yen
* Euro strengthens (New throughout; updates to U.S. market open, changes byline, dateline, previously LONDON)
By Stephanie Kelly
NEW YORK, Feb 1 (Reuters) - The dollar failed to hold onto its gains against a basket of currencies on Thursday, the day after the Federal Reserve said it expected inflation to rise this year.
The greenback also pared its gains against the yen as U.S. and European stocks fell.
In January, the dollar clocked in its worst monthly performance since March 2016, falling 3.25 percent.
The Fed left interest rates unchanged on Wednesday but bolstered expectations that they would continue to rise by saying inflation was likely to accelerate this year.
The dollar index, which tracks the greenback against six major currencies, rose briefly after the announcement and climbed again overnight in Asian trading.
However, the index later pulled back and was down 0.11 percent at 89.031 at 10:00 a.m. EST (1500 GMT).
The dollar also pared its gains against the yen in morning trading. It was up 0.29 percent at 109.49 yen, compared with 109.74 yen at around 6:30 a.m. EST.
The dollar hit a four-month low of 108.27 against the yen on Friday.
David Gilmore, a partner at Foreign Exchange Analytics in Connecticut, said a broad selloff in world stocks on Thursday had made investors cautious. U.S. stocks opened lower after a string of lackluster earnings and the Fed's comments on Wednesday.
"Markets are on pins and needles about stocks, given the correction this week," he said. "Very often we see the yen strengthen when stock prices go down."
Traders are looking ahead to the U.S. government's jobs report on Friday.
The dollar has struggled this year as expected monetary policy-tightening in other parts of the world, along with stronger global economic growth, encouraged investors to put more of their money elsewhere, particularly the euro zone. The dollar index touched a three-year low of 88.438 on Friday.
Meanwhile, the euro rose against the dollar by 0.14 percent to $1.2437, supported by a survey on Thursday that showed euro zone manufacturing was booming.
The single currency reached a three-year high above $1.25 in January and ended the month up 3.54 percent amid expectations that the European Central Bank would begin normalizing monetary policy this year.
That prospect got a boost earlier on Wednesday after last month's underlying euro zone inflation picked up pace.
Sterling rose 0.07 percent to $1.42.
The Australian dollar fell 0.62 percent to $0.8004, after its recent run-up came to an end.
Reporting by Stephanie Kelly; Editing by Lisa Von Ahn