The minutes also said "almost all" officials agreed it was appropriate to raise interest rates by 25 basis points at the meeting, while "a few" favored or could have supported a bigger 50 basis-point hike.
A number of officials said that an "insufficiently restrictive" policy stance could stall recent progress on moderating inflation pressures, according to the minutes, suggesting they are prepared to move rates up further than their December forecast of 5.1%.
U.S. central bankers raised interest rates by a quarter-point, moderating their action after a half-point hike in December and four consecutive jumbo-sized 75 basis-point increases. The move lifted the benchmark policy rate into a range of 4.5% to 4.75%.
Going into the meeting, money markets forecast interest-rate cuts in the back half of 2023. They have since tempered bets on the likelihood that the Fed will reverse course and start cutting rates before the end of this year.
Since the meeting, investors had lifted expectations for where rates will peak to around 5.33% ahead of Wednesday's minutes.
The shift in sentiment has also helped tighten financial conditions somewhat, potentially aiding the central bank as it fights to bring inflation under control amid a tight job market.
In the minutes Wednesday, Fed officials noted that it was important "that overall financial conditions be consistent with the degree of policy restraint that the Committee is putting into place in order to bring inflation back to the 2 percent goal."
Chairman Jerome Powell cautioned during his post-meeting press conference that ongoing rate increases were necessary and the Federal Open Market Committee would maintain a restrictive stance for some time.
Data released since the meeting pointed to stronger underlying momentum in the economy than was apparent at the start of February. Employers added more than twice as many jobs in January as economists expected, while inflation showed little sign of abating.
Cleveland Fed President Loretta Mester said last Thursday that she had seen a "compelling" economic case for a half-point increase during the last meeting, a view echoed later that day by St. Louis Fed chief James Bullard. Neither official votes on policy decisions this year.