Federal Reserve officials explicitly said they might raise short-term interest rates in December, pushing back against investors who have bet that the central bank wouldn’t move this year.

The message appeared to have the desired effect. Before the Fed released its policy statement Wednesday, traders in futures markets put about a 1-in-3 probability on a Fed rate increase this year; after the release, that probability rose to almost 1-in-2.

While the Fed kept rates steady after its two-day meeting this week, investors appeared to welcome a vote of confidence in the economy from the central bank. The Dow Jones Industrial Average rose 198.09 points, or 1.1%, to 17779.52.

Top Fed officials have been saying for months they believed the economy was nearly strong enough to tolerate an increase in the benchmark short-term rate from near zero, where it has been since December 2008. But they have hesitated to move.

The last instance was in September, when the Fed pointed to worries about turbulence in financial markets and uncertainties about growth overseas—particularly in China—as reasons to stay put.

“They are trying to tell us that December is still their base case,” said Roberto Perli, an analyst at Cornerstone Macro, a research firm that advises investors.

Market and international developments have turned in the Fed’s favor in recent weeks. The People’s Bank of China last week cut short-term lending rates in an effort to boost growth in the world’s second-largest economy. European Central Bank President Mario Draghi suggested he might extend a bond-purchase program in an effort to stimulate his region’s economic growth rate.

The moves sparked a global stock-market rally and could support world-wide growth. The Dow is up 6% since the Fed met last month, a sign financial-market stress has dissipated.

The Fed responded Wednesday by playing down its earlier-stated concerns. Officials struck from their policy statement a sentence introduced in September that pointed to market turbulence and global developments as potential restraints on U.S. economic activity. As those concerns recede, the Fed has fewer impediments standing in the way of a rate increase.

Though not mentioned in their statement, officials likely took note in their meeting of the recent progress toward an agreement between Congress and the White House on a federal budget and raising the government’s borrowing limit. If enacted, the budget and debt-limit resolution would reduce uncertainty about the fiscal outlook and boost government spending and short-term economic growth.

Officials pointed specifically in the policy statement to their Dec. 15-16 meeting as a moment when they might act on rates. Individual officials have signaled before that they expected to move before year-end, but the Fed’s policy-making committee hadn’t previously pointed so explicitly in an official statement to the potential timing of a rate increase.

In a late-September speech, Fed Chairwoman Janet Yellen said she expected to move by year-end. Investors had come to doubt it, in part because of resistance Ms. Yellen faces internally from colleagues who want to hold off; in part because inflation has been persistently low; in part because the Fed has already delayed several times; and in part because economic data appeared to take a turn for the worse since she spoke.

Most notably, the Labor Department reported early this month that hiring slowed in September and was less than previously reported in August and July.

Though the Fed wanted to send investors a wakeup call with Wednesday’s statement, it also didn’t commit to a December move.

Officials repeat regularly that their decision is “data-dependent.” The Fed will see two more monthly jobs reports—including one next week—before officials need to decide.

The sentence that investors homed in on in the statement was highly conditional and helps explain why futures markets still put the chance of a move as the rough equivalent of a coin flip.

The Fed said in deciding whether to raise rates “at its next meeting” it would “assess progress—both realized and expected—toward its objectives of maximum employment and 2 percent inflation.”

Having pointed explicitly to the December meeting, the Fed has potentially set itself up for criticism if it doesn’t follow through.

“Money is free right now and it is causing too many excesses in investing and lending,” Bank of Tokyo-Mitsubishi economist Christopher Rupkey said in a note to clients. “Everyone has a job. It’s time for the Fed to get going.”

Ms. Yellen is planning to be more outspoken in the lead-up to this decision, after staying mostly silent before the September meeting as a cacophony of other Fed officials weighed in on whether they thought the central bank would or should move. She is set to testify before Congress next week on financial regulation and in early December on the economy, and she delivers a speech to the Economic Club of Washington before the next meeting.

Ultimately, the Fed’s plans could be scrambled again.

U.S. economic data have been unsteady, a point officials acknowledged in their statement Wednesday. In addition to the disappointing jobs data, they noted expectations for future inflation—as measured in bond markets—had receded “slightly” further in recent weeks, a sign investors don’t expect a rebound in consumer prices soon.

Fed officials watch inflation expectations closely, because expectations can affect the prices individuals, businesses and investors actually demand for goods and services.

Fed officials repeated that they won’t raise rates until they become “reasonably confident” inflation will raise to their 2% objective after running below it for more than three years.

They also want to see “some further improvement” in the job market.

Jeffrey Lacker, president of the Federal Reserve Bank of Richmond, dissented, as he did in September. He wanted to raise the Fed’s target interest rate, called the federal-funds rate, by a quarter-percentage point.

Write to Jon Hilsenrath at jon.hilsenrath@wsj.com