WASHINGTON — Federal Reserve officials struggled at their September meeting to come to terms with persistently low inflation. But in the end, they decided that they should continue to signal the possibility of a third rate interest hike this year.

The minutes of their discussions, released Wednesday, show that a group of Fed officials worried that low unemployment could result in a quick rebound in inflation and favored a third rate hike in 2017. Another group believed that no further increases were called for in the near term.

Economists are split over whether the Fed will raise rates again in December. Some see another rate hike as likely. Others think that if inflation does not start to climb, the Fed will remain on hold.

The Fed has its next meeting Oct. 31-Nov. 1 before a final 2017 meeting in mid-December.

Earlier in the year, Fed Chair Janet Yellen and other Fed officials pointed to transitory factors such as falling prices for mobile cellphone plans as a reason why inflation was moving farther from the Fed’s 2 percent inflation goal. But with the low inflation persisting, she and other officials have recently acknowledged that perhaps something more long-lasting may be happening.

The minutes of the Fed’s September meeting revealed that the mystery over inflation was a key talking point during the two days of discussions.

“Many participants expressed concern that the low inflation readings this year might reflect not only transitory factors, but also the influence of developments that could prove more persistent,” the minutes said. “A few of these participants thought that no further increases in the federal funds rate were called for in the near term.”

However, another group of Fed officials continued to express worries that inflation could rebound very quickly, given low unemployment. The jobless rate in September fell to a 16-year low of 4.2 percent after having been at 4.4 percent at the time of the Fed’s discussions.

The group worried that low unemployment might spark higher wage demands. Rapidly rising inflation pressures could then force the Fed to begin hiking rates more quickly and run the risk of pushing the country into a recession.

The Fed’s key rate is currently at a still-low level of 1 percent to 1.25 percent after two quarter-point rate hikes this year in March and June.