June 2 (Reuters) - Federal Reserve Bank of Cleveland President Beth Hammack said Tuesday that the U.S. central bank may need to act "soon" to combat inflation pressures that are already too high and are on a worrisome trend.

"Based on the data, I'm more concerned about the growing risks of persistently elevated inflation than the risks to full employment and also that monetary policy may not be sufficiently restrictive to bring inflation down to 2 percent," Hammack said in a speech prepared for delivery before the City Club of Cleveland.

"If we wait for definitive evidence that high inflation has become embedded in the economy, it may require larger policy adjustments, at greater cost," the official said.

For now, "it's reasonable to keep rates steady given the uncertainties around the economic outlook. But if recent trends continue, it may soon be appropriate to act," the official said.

The central bank's interest-rate-setting Federal Open Market Committee meets on June 16-17 in a meeting that will almost certainly see the officials hold their interest rate target steady at between 3.5% and 3.75%. Hammack holds a vote on the FOMC this year.

It will be the first gathering held under the leadership of Kevin Warsh, who came to office pushing a case to cut interest rates that few believe stands up to the current economic environment, where price pressures have been mounting after standing above the Fed's 2% inflation target for years.

Inflation's upward draft has intensified due to the U.S.-Israeli war against Iran, which has gummed up global energy flows. That's pushed up inflation from already high levels, and many in the Fed have begun to speculate about the possible need to hike interest rates at some point if inflation relief does not soon arrive.

Interest rate futures markets are eyeing a rate increase at some point down the road for the Fed.

In her remarks, Hammack said "the picture for inflation is not encouraging. Inflation is too high and is moving higher," and data shows "relatively broad-based price pressures across goods and nonhousing services."

"There is a growing risk that inflation could remain elevated if energy costs do not come down quickly and if businesses feel they have no choice other than to raise prices," Hammack said. The official also said inflation was being driven by electricity costs, health insurance and software.

Meanwhile, the broader economy is showing resilience and the labor market is stable with a jobless rate near full employment, Hammack said, adding "measures of financial conditions are supportive of growth rather than holding it back."