* Dollar index rises for 4th straight session
* Fed to keep buying $85 bln in bonds per month
* Fed says financial conditions looser than in September
NEW YORK, Oct 30 (Reuters) - The dollar rallied against the euro and yen after the Federal Reserve said on Wednesday it will keep its stimulus for the economy in place but dropped a reference to tightening financial conditions. Traders bought back the U.S. currency after the widely expected decision, having recently piled on bearish bets on expectations the Fed will not begin cutting back its $85 billion per month asset purchases until next year. The Fed acknowledged weaker economic prospects, due in part to a partial government shutdown earlier this month. But it also said the labor market has shown "some" further improvement and dropped a reference to a "tightening of financial conditions observed in recent months" from its list of risks to the outlook. "The fact that the Fed took out the statement on financial market tightness to me seems quasi-hawkish," said Boris Schlossberg, managing director at BK Asset Management in New York. "The Fed is essentially hinting at the fact that they may taper sooner rather than later. Before, the market was expecting tapering in March and now it could very well be December. The dollar is gaining as a result of this." The euro fell 0.2 percent to $1.3726, having earlier risen after data showed a jump in euro zone sentiment in October. The single currency hit a 23-month peak of $1.3832 on Friday and traders said the euro's failure to make a sustained break above $1.3800 left it vulnerable to a correction. The dollar was up 0.5 percent at 98.62 yen, after hitting a near two-week high of 98.67 yen, according to Reuters data. The Fed's comments are consistent with current expectations for an early 2014 tapering, said Vassili Serebriakov, currency strategist at BNP Paribas in New York. "The reason that the dollar strengthened after the statement was that the market was short dollars before the meeting, and traders are just basically unwinding that position," he said. The dollar index, which tracks the greenback against six major currencies, rose for a fourth straight session, gaining 0.2 percent to 79.773, moving further away from Friday's nine-month low of 78.998. Earlier, data showed U.S. private-sector employers hired the fewest workers in six months in October while tepid domestic demand kept inflation benign last month, suggesting the economy was still in need of stimulus.