(Reuters) - U.S. Federal Reserve Governor Michelle Bowman on Tuesday reiterated her view that holding the policy rate steady "for some time" will likely be enough to bring inflation under control, but also repeated her willingness to raise borrowing costs if needed.

"Inflation in the U.S. remains elevated, and I still see a number of upside inflation risks that affect my outlook," Bowman said in remarks prepared for delivery in London.

Supply-chain improvements and a surge in labor supply from immigration, both of which helped push down inflation last year, are unlikely to continue, she said. Regional conflicts could put upward pressure on energy and food prices; looser financial conditions or fiscal stimulus could stoke inflation as well, she said.

And immigrants' housing needs, along with continued labor-market tightness, could also push up on prices, she said.

"Should the incoming data indicate that inflation is moving sustainably toward our 2% goal, it will eventually become appropriate to gradually lower the federal funds rate to prevent monetary policy from becoming overly restrictive," she said.

However, she said, the economy is "not yet" at that point, adding that she will "remain cautious" in her approach to monetary policy, and predicted that central banks in other countries may loosen policy sooner or more quickly than the Fed.

Bowman is one of the Fed's most hawkish voices, and her remarks on Tuesday were no exception.

The Fed earlier this month kept the policy rate in the 5.25%-5.5% range that it has held it at since last July. Fresh projections showed no Fed policymaker expected to raise rates from here, and the median policymaker sees just one rate cut before the end of the year.

"Looking ahead, I will be closely watching the incoming data as I assess whether monetary policy in the U.S. is sufficiently restrictive to bring inflation down to our 2% goal over time," Bowman said.

So far this year there has been just "modest further progress" on inflation, she said. "I expect inflation to remain elevated for some time."

(Reporting by Ann Saphir in Berkeley, California; Editing by Matthew Lewis)

By Ann Saphir