* Further easing depends on economy's evolution: Dudley

* Says gasoline prices 'definitely' a risk (Rewrites with comments on QE3)

By Jonathan Spicer

MELVILLE, New York, March 19 (Reuters) - The U.S. Federal Reserve has not yet decided whether to embark on a third round of quantitative easing, or QE3, though it remains an option, an influential Fed official said on Monday.

New York Fed President William Dudley, a close ally of Chairman Ben Bernanke, painted a mixed picture of the U.S. economy, tempering recent signs the recovery is gaining speed with warnings that it could just as easily stall out.

"Nothing has been decided," he said of QE3, in which the Fed would make large-scale asset purchases in an attempt to lower rates and give the economy another controversial shot of adrenaline.

"It all depends on how the economy evolves," Dudley added. "It's about costs and benefits, and if we get to a point where we think the benefits of another program of QE outweighs the costs, then we'll certainly do so."

Dudley, like Bernanke in recent testimony to Congress, defended the central bank's ultra-easy policy stance but seemed to temper any talk of exactly what more it was prepared to do to help along the recovery and ratchet down the unemployment rate, which remains high 8.3 percent.

After a meeting in Washington last week, the Fed's policy-setting committee made no policy change and gave few clues how it interpreted some recent jobs growth, coupled as it has been with worries over GDP growth and oil price-driven inflation.

Dudley said U.S. economic activity is not yet strong or sustained enough to put a dent in the economy's "slack," which is keeping many Americans out of work some three years after the deep recession ended.

"The incoming data on the U.S. economy has been a bit more upbeat of late, suggesting that the recovery may be finally establishing a somewhat firmer footing," Dudley said, citing expanding GDP late last year, payrolls, sales of motor vehicles, and somewhat firmer housing starts.

"While these developments are certainly encouraging, it is far too soon to conclude that we are out of the woods," Dudley, a policy dove with a permanent vote on the Fed's policy-setting committee, told a gathering of the Long Island Association.

GASOLINE AND OTHER HEADWINDS

The U.S. central bank has kept interest rates near zero since late 2008 and bought $2.3 trillion in long-term securities to help revive the economy after the 2007-2009 recession.

Upbeat data so far this year has tempted some, including some Fed policymakers, to say the recovery is well underway and that the Fed will take no further steps.

Yet Bernanke and others have said more bond purchases remain an option. Last year, Dudley was among the most vocal about the efficacy of buying mortgage-based securities to help revive that sector of the economy.

Dudley warned that higher gasoline prices are "definitely" a risk to the world's largest economy, which is heavily dependent on consumption.

"The upward pressure on prices caused by rising gasoline are offset by downward pressure on prices caused by all the excess slack in the U.S. economy," he said. "It's very hard to have an inflation problem when compensation costs are rising quite slowly."

The annual rate of core inflation, Dudley argued, "has peaked and we expect it to begin to decline later this year." He added that inflation expectations "remain well anchored."

Besides gas, other headwinds include impediments to the housing sector, fiscal drags at the federal and state levels, and risks that foreign growth is weaker than expected, Dudley said.

Asked about a Fed expectation to keep rates low through late 2014, Dudley said: "We view this as the best path to an early-as-possible economic recovery ... and the earliest normalization in short term rates."

Bernanke, who along with Dudley spear headed the Fed's unprecedented and easy policy steps, is set to deliver a public lecture on Tuesday. (Editing by Padraic Cassidy)