WASHINGTON (Reuters) -Only "a couple" of officials at the Federal Reserve's June 17-18 meeting said they felt interest rates could fall as soon as this month, with most policymakers remaining worried to some degree about the inflationary pressure they expect to come from President Donald Trump's use of import taxes to reshape global trade.

Trump has demanded immediate cuts, and called for Fed Chair Jerome Powell to resign, but the minutes showed only narrow support for a reduction in borrowing costs among the Fed's 19 policymakers.

"Most participants" at the Fed's meeting did anticipate rate cuts would be appropriate later this year, with any price shock from tariffs expected to be "temporary or modest," said the minutes, which were released on Wednesday.

The document covered the deliberations at the U.S. central bank's Federal Open Market Committee meeting last month, at which officials unanimously voted to keep the benchmark interest rate in the 4.25%-4.50% range set last December.

"Participants generally agreed that, with economic growth and the labor market still solid and current monetary policy moderately or modestly restrictive, the Committee was well positioned to wait for more clarity on the outlook for inflation and economic activity," the minutes said.

While many policymakers agreed rate cuts might be appropriate later this year, there was broad division about the outlook.

"Some participants ... saw the risk of elevated inflation as remaining more prominent," the minutes said. Seven policymakers in projections issued after the June meeting anticipated no rate cuts this year.

"A few participants saw risks to the labor market as having become predominant," the minutes stated.

But officials seemed, in large part, wary to change monetary policy while so much remained up in the air about the final tariff rates that Trump intends to impose and how businesses and consumers will respond.

Fed officials "agreed ... it remained appropriate to take a careful approach in adjusting monetary policy," according to the minutes.

The comments in the minutes were reflected in the interest rate projections issued after the two-day meeting, with the median rate outlook pointing to two quarter-percentage-point cuts by the end of 2025. Investors expect an initial cut at the Fed's meeting in September and a second one in December.

Fed Governor Christopher Waller and Fed Vice Chair for Supervision Michelle Bowman have since said they felt rates could fall as soon as the July 29-30 meeting, but a recent stronger-than-expected jobs report has led investors to put the odds of an imminent rate cut at close to zero.

Powell's term as Fed chief lasts until May 15.