Traders have focused on whether the Fed will increase rates for the first time in nearly a decade at its meeting later this month. Rosengren, who does not vote on the Fed's policy making committee this year, echoed other bank officials in saying he does not foresee a large effect from the first rate hike, but places more importance on the later trajectory.
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Rosengren expects the Fed will move rates higher more gradually than in previous tightening cycles. He added that the slow pace of inflation allows rates to climb slowly.
Over the weekend, Fed Vice Chairman Stanley Fischer contended U.S. inflation would likely tick up as pressure from a stronger U.S. dollar fades. Speaking from a central bankers' conference, he told CNBC last week that "it's early to tell" if the Fed should raise interest rates in September.
Read MoreFed's Fischer: Too early to decide on Sept hike
Minneapolis Fed President Narayana Kocherlakota told CNBC last week that the central bank should not hike rates this year.