But some policymakers remain doubtful that the gains will appear in the form of rapid inflation and higher wages.
Those members urged their colleagues to be "patient" as they weigh future rate rises.
The views were revealed in minutes published on Wednesday from the Fed's January meeting.
The meeting, the final gathering led by former Federal Reserve chair Janet Yellen, concluded 31 January.
It preceded turmoil in the stock market that has been pinned partly on investor calculations that the Fed might raise interest rates more rapidly than anticipated.
Investors were reacting to data, including wage increases, that suggested inflation might be stronger than in recent years, prompting the Fed to raise rates more quickly.
US stocks jumped after the minutes were released, but sank again as the afternoon continued, reflecting continuing uncertainty about the bank's future course.
The Fed has been shifting away from the policies aimed at economic stimulus it enacted during the recession, including ultra-low interest rates.
The bank took no action to raise rates at its January meeting, but markets expect at least three rate rises this year, and predict the Fed will take its next action in March.
Investors are also watching carefully to see if new Fed chair Jerome Powell takes a more aggressive stance than Ms Yellen, who was viewed as moving relatively slowly to raise rates.
At the January meeting, "almost all" Fed members - more than previously - said they expect inflation to hit the bank's 2% target over the medium term, bolstering the case for future rate rises.
A number of Federal Reserve members also "marked up" forecasts for 2018 growth to reflect stronger economic data since December, according to the minutes.
However, the record showed the participants continued to hold a wide range of views about inflation and wage pressures.
While some see the possibility of rapid inflation, others see "little solid evidence" of inflation or wage pressures, the minutes said.
"They judged that the committee could afford to be patient".
Ken Matheny, executive director for US economics at Macroeconomic Advisers by IHS Markit, said the discussion was "consistent" with predictions of several rate rises in 2018.
Mr Matheny, whose firm is predicting four rate rises this year, said he expects inflation will finally hit the Fed's 2% target causing "dovish sentiments to fade".
Source: BBC News