Senate lawmakers negotiating a financial overhaul measure on Thursday rejected a proposal to include Fannie Mae (FNM) and Freddie Mac (FRE) among financially risky entities that could be liquidated.

The Senate response came almost immediately after House members agreed to it.

House members of a "conference committee" on the bill earlier agreed to an amendment, offered by Rep. Jeb Hensarling (R., Texas) to remove an exemption for Fannie and Freddie from liquidation coverage.

House Financial Services Committee Chairman Barney Frank (D., Mass.) said he accepted the amendment because it makes clear that the government has the ability to regulate Fannie and Freddie.

Frank also said he expects overall changes on government-sponsored entities like Fannie and Freddie to be completed in the next year.

The overall financial bill would give the government regulatory authority to wind down financial firms that pose an economic risk.

Republicans have argued for much of the debate on the bill that Fannie and Freddie should be eliminated or severely restricted. They have criticized the legislation for not adequately addressing issues surrounding the government-sponsored enterprises.

A spokesman for Hensarling said removing an exemption for Fannie and Freddie would be "a small step toward putting them on the same footing as other failed institutions."

-By Fawn Johnson, Dow Jones Newswires; 202-862-9263; fawn.johnson@dowjones.com