WASHINGTON (Reuters) - Federal Reserve officials worried last month that progress on inflation might have stalled and a longer period of tight monetary policy be needed to tame the pace of price increases, according to the minutes of the U.S. central bank's March 19-20 meeting at which policymakers kept a baseline view for three interest rate cuts in 2024.

"Participants generally noted their uncertainty about the persistence of high inflation and expressed the view that recent data had not increased their confidence that inflation was moving sustainably down to 2%," the minutes from the meeting said, a sentiment that may have been bolstered by data released on Wednesday that showed another surprise jump in inflation.

Fed officials are debating whether the greater risk is for monetary policy to remain too tight for too long, or for the Fed to ease too soon and fail to return inflation to its 2% target.

Some officials continued to argue that important items like housing inflation would begin to slow, with "several" saying that increases in productivity could allow growth to remain strong while inflation continued to fall.

But the minutes reflected a general concern about the status of an inflation fight that seemed well in hand at the start of the year.

"Participants noted indicators pointing to strong economic momentum and disappointing readings on inflation in recent months," while reiterating they would need greater confidence in continued disinflation before cutting rates, the minutes said.

"Some" officials said there were risks that Fed policy was "less restrictive than desired, which could add momentum to aggregate demand and put upward pressure on inflation," the minutes said - the sort of logic that could be used to defend another rate hike.

The Fed has raised its policy rate by 5.25 percentage points since March of 2022 to combat a surge in inflation.

The consumer price index (CPI) data released on Wednesday, if anything, further undermined any certainty around inflation's decline.

The U.S. Labor Department reported that the CPI accelerated to a 3.5% annual rate in March from 3.2% in February, and a separate "core" measure excluding food and energy prices stalled at 3.8%.

Fed policymakers are debating when to lower the central bank's benchmark overnight interest rate from the current 5.25%-5.50% range, where it has been since last July. They meet next on April 30-May 1.

After the release of the latest CPI data, investors pushed out their bets on the timing of an initial rate cut to September from June.

The minutes also showed the vast majority of Fed officials judged it would be prudent to slow the runoff of the central bank's massive holdings of Treasury bonds and mortgage-backed securities "fairly soon."