The Geithner's remakes were made at the Conference on the Future of Housing Finance in Washington.
There is no "clear consensus" on how to design a new system, Geithner said, but he declared the Administration would side with whoever argued for reform.
"We will not support returning Fannie and Freddie to the role they played before conservatorship, where they fought to take market share from private competitors while enjoying the privilege of government support. We will not support a return to the system where private gains are subsidized by taxpayer losses."
Geithner asked whether it was the responsibility of the government or private markets to provide insurance against losses. Without support, he said, the financial system would be unable to support mortgage lending in future recessions.
"The challenge," he said, "is to make sure that any government guarantee is priced to cover the risk of losses, and structured to minimize taxpayer exposure."
Finally, Geithner asked how the transition to a new housing finance system should be managed. He said it was imperative to begin "weaning the markets away from government programs" and to include the private market in the mortgage business. Furthermore, it is important to keep overall mortgage rates low, and to ensure consumers have access to credit at "attractive rates," he said.
While he declared the Administration would "side with those who want fundamental change," Geithner argued for bi-partisanship.
"The failures that produced the system we have today were bi-partisan. The solution must be as well," he said. "We must take this opportunity to build a more stable housing finance system that that better protects American taxpayers."