Minutes from the Federal Reserve’s March meeting showed that central bankers were preparing to shrink their portfolio of bond holdings imminently while raising interest rates “expeditiously,” two policies that will make money more expensive to borrow and spend.

The Fed is trying to cool down a hot economy, hoping to tame inflation, which is running at the fastest pace in four decades.

Central bankers raised interest rates by a quarter of a percentage point in March, their first increase since 2018 — and the minutes showed that “many” officials would have preferred an even bigger rate increase and were stalled only by uncertainty tied to Russia’s invasion of Ukraine. Markets now expect the Fed to make half-point increases in May and possibly June, even as they begin to withdraw additional support from the economy by shrinking their balance sheet.

The balance sheet stands at nearly $9 trillion — swollen by their pandemic response policies — and Fed officials plan to shrink it by allowing some of their government-backed bond holdings to expire. That will push up longer-term interest rates, helping to make mortgages and other types of borrowing pricier. Higher rates could temper consumption and business investment, leading to slower growth, more muted hiring, and weaker wage increases. Eventually, the chain reaction should help to lower price increases.

Fed officials at the meeting “expected it would be appropriate to begin this process at a coming meeting, possibly as soon as in May,” the minutes showed.

Fed officials are trying to cool off the economy at a time when it is growing quickly and the job market is rapidly improving. Employers added 431,000 jobs in March, wages are climbing rapidly, and the unemployment rate is just about matching the 50-year low that prevailed before the pandemic.

Central bankers are hoping that the strong job market will help them slow the economy without tipping it into an outright recession. That will be a challenge, given the Fed’s blunt policy tools, a reality that officials have acknowledged.

At the same time, Fed officials are worried that if they do not respond vigorously to high inflation, consumers and businesses may come to expect persistently higher prices. That could perpetuate quick price increases and make wrestling them under control even more painful.

“It is of paramount importance to get inflation down,” Lael Brainard, a Fed governor who is the nominee to be the central bank’s vice chair, said on Tuesday. “Accordingly, the Committee will continue tightening monetary policy methodically through a series of interest rate increases and by starting to reduce the balance sheet at a rapid pace as soon as our May meeting.”

Ms. Brainard’s statement that balance sheet shrinking could happen “rapidly” caught markets by surprise, sending stocks lower and rates on bonds higher. Investors also focused their attention on Wednesday’s minutes.

Besides confirming Ms. Brainard’s signal that balance sheet shrinking could begin imminently, the minutes showed that “many” meeting participants “would have preferred a 50 basis point increase in the target range for the federal funds rate at this meeting.”

While they held off on a supersized increase amid uncertainty tied to Russia’s invasion of Ukraine, officials signaled that increases above a quarter point could be appropriate if inflation remained elevated.

“All participants underscored the need to remain attentive to the risks of further upward pressure on inflation and longer-run inflation expectations,” the minutes showed.

And officials pointed to signs that rapid price increases could last.

“Many participants indicated that their business contacts continued to report substantial increases in wages and input prices that were being passed through into higher prices to their customers without any significant decrease in demand,” the minutes showed.

Factors that Fed officials thought could cause inflation to persist included “strong aggregate demand, significant increases in energy and commodity prices, and supply chain disruptions that were likely to require a lengthy period to resolve,” the minutes said.