The Fed's annual symposium in Jackson Hole, Wyoming, on Aug. 26 is seen as the next chance for it to deliver a message about policy. The central bank's chair, Janet Yellen, is scheduled to speak and Fed chairs have been known to make important policy comments at that gathering of U.S. and international bankers.
"If asked about September, they would say every meeting is live," Canally said. "But maybe they're preparing markets for thinking about perhaps raising rates in December."
While it acknowledged U.S. labor and consumer spending have improved, the Fed said inflation continues to lag its target. Economists have been watching a pickup in core CPI inflation to 2.3 percent but the Fed focuses on PCE, which is beneath its 2 percent target.
One central bank official, Kansas City Fed President Esther George, dissented on the decision to leave rates unchanged.
"They added that near-term risks to the economic outlook have diminished. That was a throw in there for the people who are looking at the buoyancy of the financial markets and saying they could raise rates. My take on that was to keep the dissents to one. Even though they upgraded their outlook on employment and consumer spending, they left inflation unchanged. That is despite the fact that it is rising," said Diane Swonk, founder of DS Economics.
Swonk said the Fed board members are more likely to want to hold off in September, than the Federal Reserve regional presidents. She said it is possible they can hike in December but there is a risk that the easing actions of other central banks in the next two months would make it more difficult for the Fed to move.
The Bank of Japan on Friday is expected to announce more asset purchases and possibly cut rates, while the Bank of England said it could ease in August because of the effects of the Brexit vote. The European Central Bank is also expected to take action in September.
"By September, we may have more easing from abroad. My sense is the board is more sensitive to that and it's not about election risk. It's about policy risk. I think December or January is more likely. Is there a chance for September? If you're data dependent, yes ... I don't think they're going to do it but you could have people chattering out there. We've seen a lot of squawking around the Jackson Hole meeting when they're at a pivotal point," said Swonk.
Treasury yields initially edged up after the Fed statement, but the two-year yield quickly returned to where it was trading at about 0.73 percent. Yields were lower along the curve, but more intense buying at the long end, resulted in a curve-flattening move. The dollar initially rose but gave back gains.
Stocks at first sold off but returned to earlier levels soon after and later turned positive in afternoon trading. The S&P 500 fell to the bottom of its recent range, an area of support at 2,158, before moving higher.
Before the statement, fed funds futures indicated about a 30 percent chance of a rate hike in September and a 48 percent chance by December. Odds were unchanged after the statement, according to Justin Lederer, rates strategist at Cantor Fitzgerald.
"This is basically what I expected, not too much. A little volatility around the statement but we dipped down and here we are again," he said of Treasurys. Lederer said the market is now focusing on the Bank of Japan's meeting Friday where it is expected to take some easing actions, including a possible rate cut and more asset purchases.
Markets had been giving relatively low odds to a rate hike, despite the Fed's commitment to raise rates this year if the economy is strong enough. Wall Street had expected a dovish message from the central bank and in CNBC's most recent Fed survey, Fed watchers have been expecting just one rate hike this year, and most likely in December.
Marc Chandler, chief currency strategist at Brown Brothers Harriman, also said December is more likely.
"For me to be convinced on a September rate hike, I would have wanted to see more dissents," he said.
"The reason I lean against it and say the bar is high, is because I think they're still worried about the international developments," he said, noting there is an Italian vote in October that could rattle markets and China's yuan becomes part of the IMF's key currency basket.
But economists at Barclays and MUFG said September was possible. Barclays economists noted the Fed has targeted two rate increases this year, and that it could boost its signaling for a September hike during the Jackson Hole speech.
After the June 23 Brexit vote, market expectations for a rate hike this year fell dramatically, with futures indicating no rate rise this year and even a chance for a rate cut in December. But a spate of better-than-expected economic reports, including June employment and retail sales, has pushed up expectations for a hike.