WASHINGTON, Jan 6 (Reuters) - The U.S. Federal Reserve should let its balance sheet start to shrink soon after an initial interest rate increase that could come as soon as March, St. Louis Federal Reserve President James Bullard said.

"We could go ahead with balance sheet run off shortly after lifting off the policy rate," Bullard said, adding that given the breadth and level of inflation the central bank should start reducing support for the economy "sooner rather than later."

(Reporting by Howard Schneider Editing by Chris Reese)