“Provided that the economy continued to perform about as expected, most participants anticipated that gradual increase in the federal funds rate would continue and judged that a change to the Committee's reinvestment policy would likely be appropriate later this year,” the minutes read.

The U.S. central bank has already begun the process of raising interest rates back to more normal levels after holding them near zero for years to buoy the economy during the financial crisis. In March, the Fed raised its benchmark interest rate for the second time in a year and said it expects two more rate hikes this year and three more next year. Given a strengthening job market and stronger business and consumer confidence, the Fed could choose to raise rates once again at an upcoming policy meeting in May or June.

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But the Fed has yet to begin significantly reducing the massive amount of Treasurys and mortgage-backed securities it purchased during the financial crisis to try to spur lending and keep interest rates low. Some observers argue that these holdings are weighing on long-term interest rates and that the Fed should not intervene so heavily in the markets.

As economic data improves, the Fed aims to gradually remove its support and let the economy stand on its own. By selling off its holdings too quickly, however, it could trigger a sudden drop in the price of those assets or a spike in interest rates, potentially upsetting markets.

The minutes showed that Fed officials mostly preferred to tie the change to the strength of the economy — and to gradually phase out reinvestments of the proceeds from the Treasury and mortgage-backed securities that mature, rather than suddenly ceasing reinvestments altogether. That would allow the Fed’s balance sheet to slowly run down in a process that is likely to take many years.

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“I think the operative word here is going to be gradual. They’re not going to want to go cold turkey,” said Josh Feinman, global chief economist for Deutsche Asset Management. “They don’t want to do anything disruptive.”

At the March meeting, Fed officials also expressed continued uncertainty about how the White House’s policies would affect the economy, with only about half of the Fed’s voting members incorporating assumptions about fiscal policy into their economic projections.

Stock markets have surged in recent months on expectations that the Trump White House will introduce measures that stimulate the economy, including slashing taxes and boosting infrastructure spending. If those policies materialize, they could stoke inflation as well as growth, potentially forcing the Fed to raise rates more quickly. Yet the administration has already faced early hurdles pushing its tax and health-care plans through Congress.

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Most Fed officials continue to believe that government policy, if it has an effect, will end up boosting growth, according to the minutes. However, several participants said that policy changes were unlikely to affect the economy until 2018, while several believed that policy changes in areas such as immigration and trade could end up weighing on growth, the minutes said.

According to the minutes, Fed officials were encouraged by progress in the global economy, including stronger growth in China and Europe. However, they also highlighted as a potential risk upcoming elections in Europe, which could appoint leaders who might favor dissolving the euro zone.

Meanwhile, the nation's economy continues to gather strength. Most economists believe the U.S. economy is strong enough to sustain gradual increases in interest rates and that the Fed should now shift its focus to restraining emerging inflation.

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A survey of private payrolls released by ADP on Wednesday showed companies added 263,000 workers in March, the largest gain since December 2014. The personal consumption expenditures (PCE) index, a measure of inflation watched by the Fed, rose 2.1 percent year-on-year in February, the largest gain in nearly five years, while the core PCE index, which excludes volatile energy and food prices, rose 1.8 percent.

According to the minutes of the March meeting, Fed officials are keeping a closer watch on inflation but don’t yet believe it is meeting their 2 percent target on a sustained basis. Fed officials have argued that the recent recovery in oil prices appears to be driving increases in inflation and that energy prices can fluctuate significantly.

The federal government is set to release its official report on employment Friday. Strong data could encourage the Fed to announce another rate hike at an upcoming meeting.

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On Wednesday afternoon, after the release of the minutes, the futures market was forecasting a 4 percent probability of a rate hike in May and a 59 percent probability of a hike in June.

Fed watchers were stunned Tuesday by news of the sudden resignation of Jeffrey Lacker, president of the Federal Reserve Bank of Richmond, who acknowledged that he had played a role in a leak of confidential information on monetary policy to a financial analyst several years ago.