Last night, Republican officials told The Times that Mr. Steele, who lost his bid for the U.S. Senate on Tuesday, has been sought out to succeed Mr. Mehlman as national party chairman. Those Republican officials said Mr. Steele had not made a decision whether to take the post, as of last night.

Other Republican Party officials said some Republican National Committee (RNC) members, including state party chairmen, have mounted a move to have Mr. Steele succeed Mr. Mehlman.

But they said that President Bush's political adviser Karl Rove, who is Mr. Mehlman's mentor, would rather see Mr. Steele serve in the president's Cabinet, perhaps as secretary of Housing and Urban Development. These officials said no one has actually offered Mr. Steele either the RNC post or a Cabinet post.

Steele spokesman Doug Heye said last night that "I don't know of any conversations that Lt. Gov. Steele has had on this topic, but I can tell you that there are many people who have said he would be an ideal candidate, based on the race he ran this year."