Updated

Senate Republicans will meet Jan. 6 to settle incoming Senate majority leader Sen. Trent Lott's fate, the day before the Senate convenes for a new session under Republican control, GOP sources said Monday.

"Republican senators are working all over their states during December, and we have not had the opportunity to come together to discuss the developments on this issue. I believe the matter to be vitally important for all Republican senators to discuss as a group, and the need for a meeting is clear," said Republican conference vice chairwoman Sen. Kay Bailey Hutchison of Texas.

"Senator Lott has apologized and is doing everything he can to make this situation right. This meeting will provide Republican senators the opportunity for a full and open discussion about Senator Lott and his ability to lead the Republican majority," she said in a written statement.

Meanwhile, President Bush does not think that Lott needs to resign his post for making racially insensitive remarks 11 days ago.

Lott's comment that the country would have been better off electing then-pro-segregation presidential candidate Sen. Strom Thurmond in 1948 was "offensive and repugnant," White House Press Secretary Ari Fleischer said Monday, but he added that Lott has apologized and rightly so.

Lott said Thurmond's segregationist platform was not the focus of his comment, but even Bush said there is no way around that interpretation. Still, Fleischer did not say that Lott should be forced out of his leadership post, which would open the way for the Senate's No. 2 Republican, Don Nickles, to take his place.

"The president does not think he needs to resign," Fleischer said of Lott, adding that Bush had not changed his position of last week. But, he added, the president does not want to get into internal Senate matters, preferring to focus more on improving race relations and bettering the lot of all Americans.

On Sunday, Nickles became the first GOP senator to call for new leadership elections.

"I am concerned that Trent has been weakened to the point that may jeopardize his ability to enact our agenda and speak to all Americans," said Nickles, who flirted with a challenge to Lott earlier this fall and could run if new elections are held.

"There are several outstanding senators who are more than capable of effective leadership and I hope we have an opportunity to choose," said Nickles.

Lott did not respond to Nickles' comments. Lott was appearing on Black Entertainment Television on Monday night "to discuss the serious issues of diversity, opportunity and race in America," said Lott spokesman Ron Bonjean.

As Bush advisers said they would not step in to save Lott's job -- with some GOP officials suggesting the president is willing to accept the consequences if Lott loses the majority leader position, quits the Senate and allows Mississippi's Democratic governor to replace him -- calls were mounting by Senate Republicans to hold a caucus and discuss the leadership of the party.

Sen. Bill Frist, R-Tenn., a potential replacement and White House favorite, said Monday that he thinks it is important for the Republican conference to meet. He would not say whether he supports a new leadership election or would back another senator.

"My Republican colleagues and I are actively engaged in deciding what is in the best interest of the Senate as an institution and the country. I am confident a consensus will emerge, but no decisions have been made yet, and I have endorsed no specific proposal at this time," he said.

With 51 Republican senators in the next Congress, it would take 26 votes to call back Lott's leadership role, to which he was elected last month.

However, Sens. Conrad Burns of Montana, John Warner of Virginia and Chuck Hagel of Nebraska said they supported a hurry-up meeting of the rank and file in view of the controversy swirling around Lott.

Republicans "must either reconfirm their confidence in Senator Trent Lott's leadership or select a new leader," Hagel said. "In the interest of the Republican Party, the president's agenda and the nation this issue must be resolved quickly."

But the possibility of a backlash could occur against those who are suggesting that perhaps Lott leave his post. Some critics have said that Nickles and Lott's votes on race issues are no different, but Nickles is merely trying to get hold of the leadership post he has long coveted.

Nickles has also complimented Thurmond, albeit not on his presidential bid.

Some are also expressing concern that Nickles, who has criticized Lott for trying to seek out allies to blunt the issue, is prolonging a fight that only seems to hurt the Republican party further.

On Sunday, Lott allies went on the Sunday talk shows brushing aside Nickles' comments that the conference meet to discuss Lott's future.

"I don't favor a conference," Sen. Dick Lugar, R-Ind., said on ABC. "I favor Sen. Lott repudiating what he said, apologizing for it, but even more importantly, having a new agenda for the Republican Party he can lead."

"We've already made that [leadership] selection. And we're going to move forward, and we're going to do so with a purpose that, prior to these remarks, probably we didn't have," Sen. Rick Santorum, R-Pa., a member of the leadership, said in a television interview.

Fox News' Carl Cameron and Wendell Goler and the Associated Press contributed to this report.