Officials were generally upbeat about the USA economy but some expressed the need to keep their options open in the need of more data pointing to strength, the minutes showed.
According to the minutes, some Fed members felt "economic conditions would soon warrant taking another (rate rise) step".
ANALYST'S TAKE: "There is clearly strong disagreement within the Fed with regards to the timing of further rate hikes", Angus Nicholson of IG said in a report.
However, the Fed did not set a date for a interest rate hike at the meeting, as is routine.
The Fed raised rates in December for the first time in almost a decade, but it has since kept rates unchanged amid financial market volatility, a global growth slowdown and tame USA inflation.
"For me it is really beginning to move slowly and on a path that allows this economy to adjust and put rates closer to where the economy is performing", she told The New York Times in April. "Members judged it appropriate to continue to leave their options open and maintain the flexibility to adjust the stance of policy based on incoming information", the minutes said.
Among the areas of concern: inflation, which remains below the committee's 2 percent target rate, partly due to declines in energy prices.
Yields on Japanese debt sunk deeper into negative territory after steady investor demand was seen at an auction of five-year government bonds.
There are still a few key indicators in the economy, however, that could force the Fed from raising rates. A few were even pushing for a July rate hike. "But the timing of that is still indeterminate", said Thomas Simons, money market economist at Jefferies. Those comments coupled with improving economic data to suggest a USA economy ready for policy normalization. The unemployment rate has remained under 5% and wages are slowly rising. Several Fed members "preferred to defer another rate increase in the federal funds rate until they were more confident that inflation was moving closer to 2 percent on a sustained basis", the minutes said.
The minutes disappointed those who had bet that the Fed could be more hawkish after comments from influential New York Fed chief William Dudley on Tuesday that "it's possible" for rates to be hiked at the September 20-21 policy meeting.
The minutes expanded on those views to show that some policy makers saw developments including the U.K.'s vote to leave the European Union as imparting longer-term uncertainty about the outlook for global growth.
Investors will be paying close attention to a speech that Yellen will give August 26 to an annual conference of central bankers in Jackson Hole, Wyo., for any further clues about the Fed's timetable for a rate increase.