June 30 (Reuters) - Federal Reserve Bank of Cleveland President Beth Hammack said on Tuesday it remains possible that she'll advocate for higher interest rates if inflation pressures don't moderate.

"We've got inflation that's too high and it's been too high for the past five years," Hammack said in an interview on CNBC. "When I look at policy, if that continues, it may mean that we need higher interest rates to bring inflation back down to target," she said.

Hammack, who is a voting member of the interest-rate-setting Federal Open Market Committee this year, declined to say when the threshold for hiking interest rates might be met, noting, "I keep an open mind walking into every meeting. I think every meeting is a live meeting, and it's important to look at the data and see where that's taking us."

Hammack also said that while she won't give firm guidance on the path of rates, it is important to tell the public where her "reaction function" is as a way to understand how to think about the monetary policy outlook.

Hammack's television interview represented her first public comments since the FOMC meeting earlier this month. That gathering, the first under new Fed Chairman Kevin Warsh, left the central bank's interest rate target range unchanged at between 3.5% and 3.75%.

While forecasts released by the Fed show officials see rate hikes this year, the policy statement pointedly omitted any so-called "forward guidance" about the future of monetary policy, reflecting Warsh's view that by giving such guidance, markets are unable to properly price the outlook on their own.

"Financial markets perform best when they react to incoming data," Warsh said at a press conference following the policy meeting on June 17. "The financial markets work less efficiently when they ask a question: How will the Federal Reserve react to that incoming information?"

Other Fed officials who've spoken in recent days have also been willing to weigh in on monetary policy. Last Thursday, New York Fed leader John Williams said that inflation is too high and that when it comes to getting inflation back to the 2% target, "the current stance of monetary policy is well positioned to do that," indicating he sees no near-term reason to raise or lower interest rates.

In the interview, Hammack said the economy is doing well right now and the job market is consistent with full employment. She said households have also been weathering the gas price surge tied to the Middle East war relatively well so far.

"I'm not seeing a lot of restraint in the economy, I'm not hearing from these businesses that interest rates or credit spreads are a reason why they're holding back from investment and growth," Hammack said.