Boston Fed President Eric Rosengren said on Monday that the Fed should raise its interest rate further as the U.S. economy rebounded from the weak first quarter.

"Economic conditions will continue to gradually improve, which in turn would justify further actions to normalize policy, continuing a gradual return to a more normal interest rate environment," he said.

"I expect that the U.S. central bank will gradually normalize monetary policy as the three conditions set out in the April FOMC minutes are met," Boston Fed president added.

Rosengren is a voting member of the Federal Open Market Committee (FOMC) this year.