By Ann Saphir

ANCHORAGE (Reuters) - San Francisco Federal Reserve Bank President John Williams on Thursday joined a growing chorus of his colleagues signaling support for a U.S. interest rate hike in coming months, saying that waiting too long could be costly for the economy.

"I think every one of our meetings should be in play in principle ... I definitely think September should be," Williams told reporters after a speech here, referring to the U.S. central bank's next policy meeting. "I think that makes sense given where the economy is."

Saying he is in no hurry to raise rates, Williams nevertheless warned that the economy could overheat if rates are kept low for too long, like a party at which the host fails to remove the punch bowl.

Williams does not have a vote on Fed policy this year, but his views are seen as influential on the policy-setting committee because of his longstanding relationship with Fed Chair Janet Yellen, his former boss at the San Francisco Fed, and his research-driven style.

New York Fed President William Dudley and Atlanta Fed President Dennis Lockhart have also in recent days made the case that the U.S. economy is in good shape and that the Fed should soon restart an expected run of gradual rate hikes that it began last December but shelved amid financial market turmoil and fears of the effects of a slowdown in China and Europe.

Their voices are especially notable against a backdrop of market bets and some analyst commentary that the Fed will never raise rates.

Williams himself fueled some of that speculation with an essay published this week calling for a recalibration of the Fed's long-term goals given a growing body of research suggesting U.S. growth has permanently slowed.

Williams on Thursday told reporters that despite his call for a longer-term rethink, monetary policy must for now be set based on current goals, including full employment and a target of 2-percent inflation.

The Fed has met the first goal and is nearing the second, he said.

He told reporters that uncertainty about exactly when the Fed will raise rates was acceptable.

"What worries me a little bit more is that there is a view out there (that) no matter what the Fed says they are not going to raise rates for a year or two," Williams said. "That's inconsistent with my understanding of the economy and also the strategy that we’ve laid out."

(Reporting by Ann Saphir; Editing by Chizu Nomiyama and James Dalgleish)