Federal Reserve officials who spent months debating their first interest-rate increase in almost a decade are turning next to the thorny question of what to do with a balance sheet equivalent to the size of Japan's economy.

A month after liftoff, turmoil in global financial markets has pushed out expectations for more rate hikes and raised concern about what tools are available to fight the next downturn. Vice Chairman Stanley Fischer has suggested the $4.5 trillion balance sheet could be maintained as a way to hold down longer-term Treasury yields while the short-term policy rate was lifted.

Fischer's idea—discussed in a Jan. 3 speech partly on strategies for pulling the short-term rate away from zero—was taken up in more practical terms by New York Fed President William C. Dudley on Friday. Reinvesting maturing bonds and putting off a reduction in the balance sheet until the federal funds rate is raised somewhat higher "makes sense," Dudley said.