Federal Reserve officials thought inflation was still receding, though that process was expected to be "somewhat uneven," according to minutes released on Wednesday from the Fed's policy meeting last month.

Why it matters: That characterization came before new data that showed yet another month of hotter-than-expected inflation — a sign that faster price increases in key parts of the economy will take longer than anticipated.

What they're saying: Nearly all Fed officials thought it would be "appropriate to move policy to a less restrictive stance at some point this year if the economy evolved broadly as they expected," according to the minutes from the March 19-20 policy meeting.

• "In support of this view, they noticed that the disinflation process was continuing along a path that was generally expected to be somewhat uneven," the minutes show, signaling that Fed officials did not see progress on inflation stalling out at that point.
• A few officials said that the hotter inflation readings were due to seasonality quirks, but some others said the inflation jump was "relatively broad based and therefore should not be discounted as merely statistical aberrations."

The big picture: The third-straight hot inflation report released earlier on Wednesday adds to evidence that the data earlier this year was not a fluke.

• As of that meeting, a narrow majority of officials still expected to slash rates three times this year. But recent developments, like that strong inflation data, likely tempered those expectations.
• Officials said in the minutes that if the disinflation process did slow, it was possible they would maintain interest rates at their current level.
• Alternatively, they noted that they could cut rates "in the event of an unexpected weakening in labor market conditions."

The intrigue: Staff economists at the Fed said their economic projection in March was "stronger" than that in January, primarily reflecting a bigger population "due to a boost from immigration."

What we're watching: Fed officials also discussed at last month's meeting plans for when they might slow down the shrinking of its multi-trillion dollar balance sheet.

• The "vast majority" of officials thought it would be "prudent to begin slowing the pace of runoff fairly soon," the minutes read.
• The minutes said that generally, officials said they favored slowing the monthly pace of balance sheet runoff by "roughly half" from the current pace.

Go deeper: Odds of a June rate cut fade as March inflation numbers come in hot

Editor's note: This story has been updated with additional details and developments.