Interest rates in the world's largest economy have been kept at close to 0% since late 2008, at the start of the financial crisis.
Now, officials must determine when the US economy is healthy enough to grow without help from the Fed.
Some said mid-2015 would be best, while others suggested later, in 2016.
"Several participants judged that the economic data and outlook were likely to warrant beginning normalisation at the June meeting," read the minutes of the Fed's last meeting, which was held from 17-18 March in Washington DC.
"However, others anticipated that the effects of energy price declines and the dollar's appreciation would continue to weigh on inflation in the near term, suggesting that conditions likely would not be appropriate to begin raising rates until later in the year, and a couple of participants suggested that the economic outlook likely would not call for liftoff until 2016."
The Fed must balance two competing priorities: the desire to maximise employment in the US economy, while also keeping prices in check.
Some Fed officials worry that if rates are kept too low for too long, it could lead to difficult-to-control inflation.
However, recent economic data has indicated that prices in the US economy are not rising significantly, and chair Janet Yellen has said she is still concerned about sluggish wage growth in the jobs sector.
At the end of the Fed's meeting in March, the central bank said it would no longer be "patient" in determining when to raise rates, but added that it would wait until it saw "further improvement" in the US labour market before a hike.
"In sum, the minutes reflect an FOMC [Federal Open Market Committee] that agrees in very broad terms about raising rates, but is far from reaching a consensus on the timing or what is the appropriate trigger for the timing of liftoff," said Ward McCarthy, chief US economist at Jefferies bank, in a note to clients.
Officials at the US's central bank were split about when to raise interest rates, latest minutes released by the Federal Reserve have revealed.