By Ann Saphir

AUSTIN, Texas (Reuters) - The case for raising U.S. interest rates has strengthened in recent months, a top Federal Reserve official said on Friday, but long-term headwinds to economic growth mean the central bank will raise rates only very slowly.

"The Fed can afford to be patient and deliberate in its actions," Dallas Fed President Robert Kaplan told reporters in Austin on the sidelines of a conference sponsored by Mission Capital. Most importantly, he added, "the likely path of rates is going to be flatter, much flatter than we’ve ever experienced historically."

Recent labor market reports suggest the job market is still improving, Kaplan said, and while inflation is making "frustratingly slow" progress toward the Fed's 2-percent goal, he expects it will gradually rise over the next couple of years.

A weaker-than-expected reading on activity in the services sector earlier this week underscores the fact that while the Fed has kept rates very low for years, monetary policy is not as accommodative as many may think.

"On balance I don’t see that the economy is overheating here," he said.

Kaplan does not have a vote this year on Fed policy but will take part in discussions when policymakers meet on Sept. 20-21 to discuss their next move.

Traders in short-term interest-rate futures see only a one in five chance of the Fed raising rates then. Kaplan suggested that using those probabilities as a barometer of the likelihood of a Fed move would be a mistake.

"I think the markets have gotten plenty of notice that we are looking for opportunities to remove accommodation," he said. "I think we are just going to have to debate this out over the next few months as to what the appropriate next steps are."

(Reporting by Ann Saphir; Editing by Chizu Nomiyama)