WASHINGTON  A lone dissenter on the Federal Reserve’s policy-making committee warned Friday that the central bank’s monetary strategy could backfire and touch off a new boom-and-bust cycle.

Thomas M. Hoenig, the president of the Federal Reserve Bank of Kansas City, dissented on Tuesday when the Federal Open Market Committee voted 9 to 1 to invest proceeds from the Fed’s mortgage-bond portfolio in longer-term Treasury debt. The decision was the Fed’s clearest signal yet that its confidence in the pace of the recovery was waning.

“Monetary policy is a useful tool, but it cannot solve every problem faced by the United States,” Mr. Hoenig told local Chamber of Commerce members in a speech at the University of Nebraska, Lincoln. “In trying to use policy as a cure-all, we will repeat the cycle of severe recession and unemployment in a few short years by keeping rates too low for too long.”

Mr. Hoenig added: “I wish free money was really free and that there was a painless way to move from severe recession and high leverage to robust and sustainable economic growth, but there is no shortcut.”