NEW YORK (TheStreet) -- The Federal Reserve isn't in as much of a hurry to raise interest rates as many people thought.

The central bank admits as much in the minutes of the June policy meeting, which were released Wednesday.

"Most participants judged that the conditions for policy firming had not yet been achieved," the minutes say. "A number of them cautioned against a premature decision."

There were several mentions of the potential for a contagion related to Greece's debt woes, and a longish section emphasizing that the central bank's professional staff expects inflation to stay below the Fed's 2% annual target rate through 2016 and 2017.

One would be a reason to keep rates low, making money cheap in case it's needed to deal with Greece's fallout. The other is a reason to not rush to raise rates, since the improving U.S. economy isn't showing obvious sign of a need to tap the brakes.

All this lends credence to the move in futures markets in the last few weeks, which are now signalling that the Fed will wait until January to begin raising rates for the first time since 2006. There are more reasons to keep the money flowing for now than there are to make cash more expensive right away, at least judging by the minutes themselves.

Among the Fed's concerns: Greece, the market woes in China, the three-decade low in productivity growth and the weak corporate investment that has helped produce that sluggishness, the minutes say. These offset the April and May bump in consumer spending and car sales, and even the judgment of "several..participants" that "labor market slack had already been largely eliminated."

"Recent developments in Greece and China and the decline in global commodity prices, particularly if they persist, will undoubtedly have an impact on Fed behavior," said Mike Collins, manager of the $9.2 billion Prudential Total Return Bond Fund. Even if the central bank codes its answer, referring to changes in the value of the dollar that reflect international crises, the influence of world events will still be there, he said.

But other economists pointed to models insisting that Greece is likely to have little to no impact on the U.S. economy, and won't even much disrupt the recovery in northern Europe. If the central bank is rational, the improving U.S. data on consumer spending, jobs and income should point to a rate hike as soon as September.

"China and Greece could spook the Fed, leading some to lobby for waiting until December or 2016," Moody's Analytics economist Ryan Sweet said just before the 2 p.m. release of the minutes. But "we don't expect Greece or the drop in China's stock market to leave a noticeable mark on the U.S. economy."

The minutes do make clear that an increase of the near-zero Fed funds rate the central bank adopted in 2008 is coming, and relatively soon.

A large section of the minutes deals with how the central bank can communicate that when it moves, it will move slowly. The Fed plans to release "implementation notes" explaining the mechanics of its upcoming market moves when it does decide to change policy, the minutes say. 

Fed chair Janet Yellen is speaking Friday and will have a chance to answer the question of how much attention the Fed should pay to China and Greece.