U.S. inflation is still too high, Federal Reserve (Fed) Chair Kevin Warsh said Friday, suggesting the central bank may have to raise interest rates in the coming months to bring it down, a clearer signal than he had sent previously about his economic outlook.

In his first high-profile speech at the Fed's annual conference in Jackson Hole, Wyoming, Warsh acknowledged that recent U.S. reports show that inflation has cooled a bit, but "they do not tell me that underlying trends have meaningfully improved."

"We must be confident that underlying inflation is moving to our objective, clearly and at sufficient speed," Warsh said. "Otherwise, we have work to do."

Comments from the new Fed chair appeared to reassure Wall Street that fighting inflation remains the priority for the central bank. Warsh did not imply in his speech that a rate hike is imminent, but at the same time, he seemed to dismiss perceptions that inflation is not a threat.

He pointed to data showing that inflation remains stubbornly above the central bank's 2% target. Warsh replaced Jerome Powell in late May after his predecessor's term ended.