In prepared remarks for the Senate Committee on Banking, Housing & Urban Affairs, Geithner said policies that shaped financial decisions for decades should be reversed.
"Our goal is not for every American to become a homeowner," he said.
"We are committed to a system in which the private market -- not American taxpayers -- bears the burden for losses" in the housing market, he said.
Taxpayers have been supporting two government-sponsored enterprises, the Federal National Mortgage Association and the Federal Home Loan Mortgage Corp., which guarantee mortgage loans and sets the pace on appropriate lending practices.
Geithner, however, said regulators dropped the ball.
"Taxpayers (were left) responsible for much of the risk incurred by a poorly supervised housing finance market," he said, adding, "These were avoidable mistakes."
Going forward, he said, "We are committed to a system in which the private market -- not American taxpayers -- bears the burden for losses."
He said, "I want to emphasize that it is very important that we wind down Fannie Mae and Freddie Mac at a careful and deliberate pace."
Pointedly, although the government took over the two mortgage giants in September 2008, their role in the mortgage market has increased, as lending has become tighter. "In the wake of the financial crisis, private capital has not sufficiently returned to the mortgage market, leaving Fannie Mae, Freddie Mac, FHA (Federal Housing Administration) and Ginnie Mae (Government National Mortgage Association) to insure or guarantee more than nine out of every 10 new mortgages," Geithner said.