House Republicans pressed Treasury Secretary Timothy Geithner Tuesday to release a detailed plan to unwind remaining taxpayer exposure to American International Group (AIG).

Geithner said he would give lawmakers a broad plan for how the government will unwind its holdings.

Under the Troubled Asset Relief Program, the government still holds $36 billion in AIG stock for a 61% stake in the monoline, according to the special inspector general for TARP.

Rep. Judy Biggert, R-Ill., asked Geithner if AIG, which required more than $167 billion in bailout commitments, remains largely unregulated today.

"Under the law of the land, that's true. That's how the system works," Geithner said. He added the Federal Stability Oversight Council and its agencies continue to work on systemically important financial institution designations, which could place AIG under Federal Reserve supervision.

But he gave no timeline for when the designations would be made, even as AIG continues to make bets on residential and commercial mortgage bonds.

Once under Fed regulation, AIG would be forced to hold more against risk. The AIG credit-default swap portfolio remains at $168 billion.

Geithner explained the Fed is working with foreign central banks on how to enforce the rules in a unified way.

"We negotiated uniform rules. That's not enough, because you want to make sure they're enforced on a common basis and that is a very challenging process," Geithner said. "If you raise standards in the U.S. and leave them weaker outside the U.S., risk will shift outside of the U.S., but will still affect us."

Rep. Spencer Bachus, R-Ala., said not having AIG under a regulator is a disservice to taxpayers.

Still, Geithner reiterated the TARP investments in the monoline remain on track to net taxpayers a profit.

"On current estimates, and this is a remarkable thing, the taxpayer will earn a substantial positive return on the full scope of tens of billions of dollars of exposure we took to AIG to protect the economy from its failures," Geithner said.