Treasury Secretary Timothy Geithner said on Wednesday the Obama administration was making headway in settling financial markets and said a program to cleanse so-called toxic assets from banks' balance sheets will start operating over the next six weeks.

Testifying to the Senate Banking Committee, Geithner said the U.S. financial system was starting to heal after a period of severe trauma, and he estimated that $123.7 billion was left in a financial bailout fund approved by Congress in October.

But in opening remarks, the top Republican on the panel, Senator Richard Shelby of Alabama, said there had been a massive waste of taxpayer dollars because there was no clear strategy for deploying hundreds of billions of dollars in rescue funds.

Geithner said financial companies were adjusting their operations in ways that will make them less vulnerable to shocks like the one they have gone through.

Leverage has declined, the most vulnerable parts of the non-bank financial system no longer pose the same risk, and banks are funding themselves more conservatively, he said.

He said so-called public-private partnerships, which would pair government and private-sector funds to buy troubled assets from banks to free up lending capacity, should be ready to operate within weeks.

Working with the Federal Reserve and the (Federal Deposit Insurance Corp), we expect these programs to begin operating over the next six weeks, he said.

Much of Geithner's lengthy opening remarks was a recap of the many programs the government has implemented, both during the former Bush administration and since President Barack Obama took office in January.

He said a presidential task force set up to deal with the collapsing U.S. auto industry would keep working with General Motors Corp right up until a June 1 deadline. GM may need to enter bankruptcy to restructure, as Chrysler Corp already has done.

Geithner said the Obama administration would ensure that financing remains available for remaining creditworthy auto dealers and will also try to boost demand for new cars.

(Reporting by Glenn Somerville, Editing by Neil Stempleman)

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