(Reuters) - Inflation is still too high, and the U.S. central bank has more work to do to bring it down, Kansas City Federal Reserve Bank President Jeffrey Schmid said on Tuesday, a signal that he supports keeping the Fed's policy rate steady for some time.

"Over time, I expect inflation to ease back towards the Fed's 2% objective," Schmid said in remarks prepared for delivery to the regional Fed bank's agricultural summit. "I am prepared to be patient as this process plays out."

Inflation fell rapidly in 2023 from its mid-2022 peak, and Fed policymakers began this year expecting to start cutting rates to keep policy from becoming overly restrictive. But price pressures picked up again in the first quarter, with the personal consumption expenditures price index rising 2.7% in March from a year earlier. The Fed targets 2% inflation by that measure.

"The Fed must hold back demand growth until supply can catch up and the imbalance that is driving inflation closes," Schmid said. In the face of the Fed's rapid interest-rate increases from 2022-2023, there are signs that imbalances are easing -- the labor market, he noted, "has come off a historic boil."

Increases in the supply of labor, goods and services are also making the Fed's job on inflation easier. Still, Schmid said, the Fed should not put too much weight on any one piece of data.

"I prefer a steady approach to policy, and one that dampens the volatility in financial markets rather than contributes to it," he said.

Increased U.S. government borrowing and other longer-term forces mean that interest rates could remain high for some time, he said.

With the Fed policy rate in the 5.25%-5.5% range since last July, "policy is in the correct place, and with patience we are on a path to achieve our policy objectives," Schmid said. "However, nothing is certain and continued vigilance and flexibility are necessary."

Fed Chair Jerome Powell earlier on Tuesday signaled he still expects inflation to drop further this year toward the Fed's 2% goal, but said it would likely require holding the policy rate at its current level for longer than earlier thought.

Both Powell and Cleveland Fed President Loretta Mester said they think a rate hike is unlikely, though Mester said that if inflation progress stalls, Fed policymakers would need to think about it.