Three Federal Reserve presidents called for higher interest rates on Friday, pushing back against Fed Chair Kevin Warsh's more dovish outlook as persistent inflation raises questions about whether the central bank has done enough to bring prices under control.

The clear messaging shifts the odds of a December interest rate increase higher. About 73% of investors anticipate that there will be a hike at the next meeting, according to the CME FedWatch tool.

Their comments came just two days after the Fed voted to hold interest rates steady at 3.75% to 4.0%. Warsh suggested Wednesday that rates might already be at an appropriate level, but a growing contingent of policymakers appears unconvinced.

Dallas Fed President Lorie Logan, a voting member of the Federal Open Market Committee this year, said Friday that she would like to see two more quarter-percentage-point rate increases in the near future.

"After that, it would make sense in my view to pause and examine economic and financial developments to determine what further action may be appropriate," she said at Davidson College.

Logan isn't alone in calling for tighter monetary policy. At Wednesday's meeting, Cleveland Fed President Beth Hammack and Fed Governor Lisa Cook dissented from the decision to hold rates steady, favoring a quarter-percentage-point increase instead.

Logan, who dissented at the Fed's July meeting in favor of a rate increase, supported Wednesday's decision.

The push for higher rates comes as inflation shows further signs of acceleration. Data released Thursday showed that the Fed's preferred inflation gauge rose in September as higher energy prices pushed up the cost of living.

Both headline and core inflation reached their highest annual rates since May. The report also marked the 68th consecutive month that inflation, as measured by the personal consumption expenditures price index, exceeded the Fed's 2% target.

St. Louis Fed President Alberto Musalem expressed similar concerns Friday afternoon in New York.

"Inflation is too high, exceeding the FOMC's 2% target. I perceive inflation risks are skewed toward persistent above-target inflation," he said. "I judge that additional firming of monetary policy will be necessary, and soon," Musalem said, signaling support for multiple rate increases.

He argued that acting sooner could allow the Fed to bring inflation down without inflicting unnecessary damage on the economy.

"Incremental adjustments made earlier are usually less disruptive than larger and abrupt actions taken later," Musalem said.

Richmond Fed President Tom Barkin, who will be a voting member of the committee next year, also indicated Friday that the case for higher rates was clear.

"Inflation's high, demand is solid, unemployment is relatively low. So I think the direction of travel is pretty straightforward," Barkin said on SiriusXM's Business Briefing when asked whether the Fed should lift rates again.

The Fed's latest Summary of Economic Projections, released in September, also pointed to the possibility of one more rate increase this year.

The Fed next meets Dec. 8-9, its final meeting before a more dovish group of regional Fed presidents rotates onto the rate-setting committee in January.