LONDON  The chairman of the Federal Reserve, Ben S. Bernanke, warned Tuesday that the highly unpopular job of using taxpayer money to bail out financial institutions in the United States and other countries was far from over.

One day after President Bush, at the request of President-elect Barack Obama, asked Congress to free up the second half of the money for the Treasury Department’s $700 billion financial rescue program, Mr. Bernanke cautioned that banks and other lending institutions were still not functioning properly and would probably need additional money.

“More capital injections and guarantees may become necessary to ensure stability and the normalization of credit markets,” Mr. Bernanke said during a speech at the London School of Economics.

Though the Fed chairman acknowledged that people in many countries were “understandably concerned” about pumping government money into the financial industry while often turning a cold shoulder to other sectors, he defended the effort as unpleasant but necessary.