The Obama administration on Thursday detailed its wide-ranging plan to overhaul financial regulation by subjecting hedge funds and traders of exotic financial instruments, now among the biggest and most freewheeling players on Wall Street, to potentially strict new government supervision.

The Treasury secretary, Timothy F. Geithner, outlined the plan Thursday before the House Financial Services Committee. He said the changes were needed to fix a badly flawed system that was exposed by the current financial crisis. Mr. Geithner, in his opening statement, called for “comprehensive reform. Not modest repairs at the margin, but new rules of the game.”

Included in the plan would be the establishment of one single agency “with responsibility for systemic stability over the major institutions and critical payment and settlement systems and activities.”

To that end, Mr. Geithner said: “Financial products and institutions should be regulated for the economic function they provide and the risks they present, not the legal form they take,” Mr. Geithner said. “We can’t allow institutions to cherry pick among competing regulators, and shift risk to where it faces the lowest standards and constraints.”

He did not provide details for how all this will work, saying that the proposals would be outlined over the coming weeks.

The plan, which would require Congressional approval, would give the government new powers over “systemically important” banks and other financial institutions that are so big that their collapse would jeopardize the economy as a whole.

The government would have the power to peer into the inner workings of companies that currently escape most federal supervision — insurance companies like the American International Group, multibillion-dollar hedge funds like the Citadel Group and private equity firms like the Carlyle Group or Kohlberg, Kravis & Roberts.

If regulators decided that a company had become “too big to fail,” as was the case with A.I.G. in September, they would subject it to much stricter capital requirements than smaller rivals and much closer scrutiny of its borrowing levels and its trading partners, or counterparties.