Federal Reserve officials at their most recent meeting saw an economy growing at a strong pace and inflation moving up as well, justifying continued interest rate increases.

Minutes from the March gathering of the Federal Open Market Committee showed central bankers largely hopeful about the direction in which the economy was headed, though with a few misgivings.

The meeting summary noted that "all participants" expected both the economy to strengthen and inflation to rise "in coming months." The general sentiment likely fuels belief that the Fed will continue on its path of rate hikes.

"Participants generally saw the news on spending and the labor market over the past few quarters as being consistent with continued above-trend growth and a further strengthening in labor markets," the meeting summary said.

The FOMC unanimously voted to approve a quarter-point rate hike, bringing the target range to 1.5 percent to 1.75 percent. There were some misgivings, mostly from "a couple" members who thought it would be better to wait for more evidence that inflation was progressing toward the Fed's 2 percent goal.

"With regard to the medium-term outlook for monetary policy, all participants saw some further firming of the stance of monetary policy as likely to be warranted," the summary said. "Almost all participants agreed that it remained appropriate to follow a gradual approach to raising the target range for the federal funds rate."

Markets expect the Fed to hike rates again in June and likely in September, though a fourth 2018 increase has just about a 1 in 4 chance, according to fed funds futures data.