Investors raised their expectations for higher interest rates on Friday in response to a high-profile speech by Kevin Warsh, the chairman of the Federal Reserve, in which he said that the central bank might have “work to do” if inflation remained high.

Mr. Warsh, speaking at the Fed’s annual economics conference is Jackson, Wyo., expressed his resolve to tackle inflation, while continuing to avoid committing to how the central bank would accomplish that. The central bank’s traditional tool to control an overheating economy is to raise interest rates.

“Here is my standard: We must be confident that underlying inflation is moving to our objective, clearly and at sufficient speed,” said Mr. Warsh. “Otherwise, we have work to do. That’s our job.”

The two-year Treasury yield, which is sensitive to Fed rate moves, rose roughly 0.1 percentage points on Friday. It’s the biggest one day move higher since June — a large, though not panicked, move in that market.

Stock investors typically recoil from higher Treasury yields, which flow through to higher costs for companies and consumers, but investors appeared to welcome Warsh’s comments on inflation. The S&P 500 initially fell as Mr. Warsh addressed conference attendees, before rising to a small gain for the day.

Investors lifted the probability of the Federal Reserve pushing up interest rates before the end of the year. A quarter of a percentage point increase is expected by the end of the year.

The likelihood of a quarter-point raise at the Fed’s next meeting in September moved higher, but remains a coin toss, with investors giving the outcome a roughly 50 percent chance.

“Overall, it was a deliberately hawkish speech that will put to rest any concerns about the Fed’s willingness to raise rates to restore price stability,” said Vail Hartman, an analyst at BMO Capital Markets.

Investors were also looking to Mr. Warsh’s remarks on Friday to see how the recently appointed Fed chief would explain to the markets the central bank’s moves.

Mr. Warsh restated that he would limit the Fed’s public remarks about the economic outlook. He told attendees that he hoped that reducing guidance would prompt investors to make their own decisions for where the economy was headed, sending signals to the Fed via prices in financial markets.

Some analysts have doubted the efficacy of this strategy, noting that investors always try to gauge what the Fed is going to do next, whether the central bank tells them or not. The increased uncertainty, the analysts have warned, would instead result in broadly lower asset prices and higher interest rates, as investors seek to protect themselves from the unpredictability that comes with less information.