Inflation rate is now at 1.6 percent and has fallen short from the 2 percent goal for six years, but several indicators lately suggested higher price pressures.
Some Fed officials noted their worries that higher budget deficits could raise interest rates or threaten "fiscal sustainability".
Economists predict that recently approved tax cuts and public spending will spur further growth, and possibly inflation.
"Participants did not see the steel and aluminium tariffs, by themselves, as likely to have a significant effect on the national economic outlook, but a strong majority of participants viewed the prospect of retaliatory trade actions by other countries, as well as other issues and uncertainties associated with trade policies, as downside risks for the U.S. economy", the minutes said.
The March policy meeting was the first under new chair Jerome Powell.
As a result of the strengthening economy and labor market, Fed officials expected inflation would move up in the coming months. "But a strong majority of participants viewed the prospect of retaliatory trade actions by other countries" as a downside risk.
"Participants did not see the steel and aluminum tariffs, by themselves, as likely to have a significant effect on the national economic outlook", the minutes read, "but a strong majority of participants viewed the prospect of retaliatory trade actions by other countries, as well as other issues and uncertainties associated with trade policies, as downside risks for the US economy".
Traders see a 90 percent chance for a rate hike in June, while they price in about a 75 percent chance for a third rate hike in December.
However, "a number of participants" said they expect stronger growth and inflation in the next few years, suggesting the path for interest rates "would likely be slightly steeper than they had previously expected", according to the minutes.
Since the March meeting, Fed officials have largely adopted a wait-and-see attitude to trade policy, noting it is not yet clear if the tariffs will go into effect and their eventual size if implemented. However, trade disputes, most prominently about tariffs on goods in the United States and China, are a worry.
The Fed has raised its target range for overnight bank borrowing, known as the fed funds rate, six times since late 2015.
Officials also seemed to shrug off the increase in stock market volatility in February, attributing it in part to Labor Department reports that the suggested growth in wages - and, with it, inflation - was gaining steam, which could force the Fed to raise rates faster than expected. A large body of evidence shows the purchasing power of Americans has not increased much in years.
The prevailing objective of the Fed since the Great Recession is that low-interest rates and the purchase of bonds allow businesses and consumers to operate in an environment in which the cost of money is close to zero. For several years, these have described the stance of monetary policy as "accommodative".