Some members said interest rates should only be tightened "gradually to help ensure that inflation would stabilize" around the two per cent target, the minutes showed.
However, "several other participants" in the Federal Open Market Committee (FOMC) said the rise of inflation to target might "warrant a faster pace of scaling back accommodation" by raising interest rates.
The rate-setting FOMC said: "Economic conditions will evolve in a manner that will warrant gradual increases in the federal funds rate."
The minutes also showed the bank's members expected the central bank to start unwinding its balance sheet by stopping the reinvestment of payments from matured bonds.
The minutes said: "Most participants anticipated that gradual increases 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 securities on the Fed's balance sheet were bought during the quantitative easing programme of bond-buying. The unconventional monetary policy tool was used during the financial crisis to try to push money out into the broader economy.
The US central bank currently holds around $4.5 trillion in securities, mostly in US Treasury bonds and mortgage-backed securities.
Markets were mostly unmoved, with Fed officials already having signalled they thought the balance sheet should be unwound this year.
The US dollar retained highs hit earlier in the day after employment data came in stronger than expected. The trade-weighted dollar index rose to above 100.8 points to reach its highest point since the Fed's dovish statement of monetary policy in mid-March.
The data from payrolls provider ADP showed the US private sector added 263,000 jobs during March, an increase from the 245,000 jobs added in February, and significantly higher than economists had expected.
However, data from the Institute for Supply Management showed non-manufacturing activity slowed during the month. The purchasing managers' index (PMI) showed expansion cooling as the reading fell to 55.2, below consensus expectations of 57. A reading above 50 indicates an expansion in the sector.
Benchmark US 10-year Treasury yields fell in response to the minutes, but remained little changed over the course of the day.
The Federal Reserve raised interest rates for the second time in three months on 15 March, continuing its move towards normalising monetary policy.
The Fed raised the target range for the federal funds rate to 0.75-1 per cent, while signalling it expected two more interest rate increases this year.
However, the cautious outlook in the Fed’s communications saw the dollar tumble as investors recalibrated their bets on the pace of monetary tightening.
FOMC chair Janet Yellen surprised markets by saying only a “gradual” pace of interest rate rises was appropriate.
Since then the price consumption expenditures (PCE) index of inflation, the Fed’s preferred measure, has broken through the Fed’s two per cent target. However, the target is symmetrical, allowing room for manoeuvre above and below target.