The strengthening job market left majority comfortable with raising a key short-term rate last month. Meanwhile, U.S. officials will soon confront the challenge of raising the debt ceiling to continue to fund the government.
The Fed has raised rates three times in the past six months, but that hasn't necessarily led to higher borrowing costs this year.
Monetary policymakers were also divided on the timeframe for winding down the Fed's multi-trillion-dollar investment holdings, with some arguing the central bank should announce this within "a couple of months", the minutes showed.
"These views suggest that a third rate hike this year remains a solid base case, but also that such a hike is unlikely to come before the December meeting", said Roberto Perli, an economist at Cornerstone Macro.
Neel Kashkari, president of the Federal Reserve Bank of Minneapolis, cited his concern about weak inflation as a reason that he voted against a rate increase at the June meeting.
Fed officials lowered their long-term projections for both inflation and the unemployment rate, while their projected path for interest rate increases remained mostly unchanged.
As of Wednesday afternoon, markets were projecting a 97 percent chance that the Fed would remain on hold when it meets again in July. The Fed's favored inflation measure, the core personal consumption expenditure index, grew just 1.4 percent at an annualized rate in May, below the rate that the Fed targets. Investors saw a almost 20 percent chance of another rate hike in September, and a 60 percent chance of another rate hike or two by December.
After the June meeting, Yellen said the plan would lead to "a gradual and largely predictable decline" in the assets. This assessment would take into account a wide range of information, including measures of labor market conditions, indicators of inflation pressures and inflation expectations, and readings on financial and global developments.
Because of the markets' performance and subdued volatility, a few Fed officials expressed concern about "a buildup of risks to financial stability". Any profit the Fed has at the end of the year must be sent to the U.S. Treasury.
The plan, approved in June, involves the Fed slowly reducing its holdings by gradually allowing an increasing amount of proceeds from maturing securities to be run off the books each month. The reductions would begin this year "provided that the economy evolves broadly" as Fed officials are forecasting, she said. The statement released at the meeting only indicated such a process would start this year.