By Lindsay Dunsmuir and Svea Herbst-Bayliss

WASHINGTON/QUINCY, Mass. (Reuters) - U.S. Federal Reserve policymakers on Friday headed towards their policy meeting later this month divided on whether a rate rise is in the offing, with some of the permanent voting members appearing wary of supporting an immediate hike.

Financial markets had started pricing in a greater chance of a rate hike on Sept. 21 on the back of a series of hawkish speeches. After Boston Federal Reserve President Eric Rosengren spoke on Friday, odds on a rate hike in September rose to 30 percent probability from 24 percent before his comments.

After the more dovish Federal Reserve Governor Daniel Tarullo spoke, that had fallen to a 20 percent chance.

Tarullo told CNBC he wants to see more evidence of a sustained uptick in inflation toward the Fed's 2 percent target before raising rates, an oft-repeated assertion of his that immediately dampened investor expectations that the central bank will raise rates at its Sept. 20-21 meeting.

"As inflation in my view shows that it's picking up in a sustainable way... then we'd raise rates," Tarullo said, adding there had been "so many false up and downs in the past."

There are five members of the Washington-based board of governors, including Tarullo, all of whom have a permanent vote on monetary policy and ten voting members overall.

Influential Fed Governor Lael Brainard has also repeatedly advocated against raising rates too quickly amid sluggish inflation and growth in the U.S. and globally. She is scheduled to speak in Chicago on Monday, one day before the central bank's communications blackout period takes effect.

The other five voters this year are from the regional Fed banks and include Esther George, who has long supported a rate rise and dissented at the last three of the Fed's four policy meetings at which rates were left unchanged.

WILLING TO WAIT, BUT FED SIGNALS UPWARD PATH

Tarullo's comments contrasted with those of Rosengren who said the U.S. economy increasingly faces risks if the central bank waits too much longer to raise rates.

"Risks to the forecast are becoming increasingly two-sided," Rosengren said in Quincy, Massachusetts. He added that while a slowdown overseas remains a concern, the U.S. economy has proven resilient and could even overheat if Fed policy remains unchanged for too much longer.

That said, Rosengren did not say whether he expects to back a rate hike this month or even this year.

Financial markets are pricing in a December rate hike. Chair Janet Yellen said in an appearance at Jackson Hole, Wyoming, two weeks ago said that "the case for an increase in the federal funds rate has strengthened in recent months."

That view was echoed on Friday by another Fed official, Dallas Fed President Robert Kaplan, who nevertheless added that long-term headwinds to economic growth mean the central bank can afford to raise rates very slowly.

"The Fed can afford to be patient and deliberate in its actions," Kaplan told reporters in Austin, Texas.

(Additional reporting by Ann Saphir in AUSTIN and Jonathan Spicer in NEW YORK; Editing by Chizu Nomiyama and David Chance)