The Federal Reserve should keep buying mortgage bonds even if it starts reducing purchases of Treasuries, and in the future it would be wise to not sell them altogether, said Eric Rosengren, president of the Federal Reserve Bank of Boston.

"I'd rather be more focused on Treasuries first and MBS second, and possibly keeping the MBS on our books," he said.

The comments from Rosengren, a dovish voter on monetary policy this year, shed some light on how the Fed might reduce its asset purchases and, longer-term, how it could adjust its "exit strategy" for getting rid of the assets altogether.