Earlier in the day, the chairman of the Republican Party and a leading GOP senator had called on Reid to give up his post.

"Over the years, I have had an opportunity to work with Majority Leader Reid," Rep. Barbara Lee, chairwoman of the caucus, said in a statement.

"Senator Reid's record provides a stark contrast to actions of Republicans to block legislation that would benefit poor and minority communities."

Lee added that she looked forward to Reid serving as majority leader.

"There are too many issues like the economy, job creation and energy for these regrettable comments to distract us from the work that must be done on behalf of the American people," she said.

The remarks were "embarrassing and racially insensitive," Sen. John Cornyn, R-Texas, head of the GOP's Senate campaign arm, said in a statement to CNN.

Republican Party Chairman Michael Steele, on NBC's "Meet the Press," said, "Racism and racist conversations have no place today in America."

Steele was also on the defensive for a remark he made last week that members of both parties have called a racial slur.

Reid's office made clear he has no plans to step down.

"Senator Reid will stay in his position as majority leader and will run for re-election," his spokesman said.

"As the leader in the fight to pass the Voting Rights Act and legislation banning hate crimes, Senator Reid has a long record of addressing issues that are important to the African-American community. His Republican critics who are looking to politicize the issue can't say the same."

Reid is already embroiled in a tough re-election campaign in his home state to stay in the Senate. Only one-third of Nevada voters have a favorable opinion of him, while 52 percent have an unfavorable opinion of the four-term senator, according to a survey by Mason-Dixon Polling and Research for the Last Vegas Review-Journal released over the weekend.

The poll was conducted January 5-7, before news of Reid's comments.

The controversy surrounds remarks published in the book "Game Change," which goes on sale Monday.

It quotes Reid as saying privately in 2008 that Obama could succeed as a black candidate partly because of his "light-skinned" appearance and speaking patterns "with no Negro dialect, unless he wanted to have one."

The authors write that "Reid was convinced, in fact, that Obama's race would help him more than hurt him in a bid for the Democratic nomination."

In a statement to CNN, Reid said, "I deeply regret using such a poor choice of words."

"I sincerely apologize for offending any and all Americans, especially African-Americans, for my improper comments. I was a proud and enthusiastic supporter of Barack Obama during the campaign and have worked as hard as I can to advance President Obama's legislative agenda," Reid added.

In his defense, he pointed to his efforts to integrate the Las Vegas Strip work force and the gaming industry, among other legislation favored by African-American voters.

After Reid called Obama on Saturday afternoon to apologize, the president said, "As far as I am concerned, the book is closed."

"I accepted Harry's apology without question, because I've known him for years. I've seen the passionate leadership he's shown on issues of social justice and I know what's in his heart," the president said.

An aide to the senator told CNN that Reid also apologized to several prominent African-American political figures, including House Democrats Lee of California and Jim Clyburn of South Carolina; the Rev. Al Sharpton; CNN political contributor and Democratic strategist Donna Brazile; NAACP Chairman Julian Bond; and the head of the Leadership Conference on Civil Rights, Wade Henderson.

Steele, the GOP's first African-American chairman, was asked by NBC whether he thinks the situation is similar to one involving former Sen. Trent Lott.

Lott lost his post as Senate majority leader in 2002 after saying the nation would have been better off if one-time segregationist candidate Strom Thurmond had been elected president.

"Oh, yeah. There is a big double standard here," Steele said. "When Democrats get caught saying racist things, you know, an apology is enough."

Cornyn, in his statement, also accused Democrats of following a double standard, and noted that they had pushed Lott to step down.

He added that Reid "has yet to clarify" his remarks. "As we await his explanation, Senator Reid should do the right thing, follow the example that he himself set in 2002, and step down as majority leader."

Gov. Tim Kaine of Virginia, chairman of the Democratic Party, shot back against those arguments.

"Anybody looking at Trent Lott's statements, praising somebody who had been a pro-segregation candidate for president, will see that there is no comparison between those comments and those of Senator Reid's," he told NBC.

Kaine said "the case is closed" after Reid's round of apologies. The comments "were in the context of praising the senator and acknowledging that the senator could be a great president, but they were still insensitive," Kaine said.

Steele, meanwhile, was asked about his remark in a Fox News interview last week that the GOP platform "is one of the best political documents that's been written in the last 25 years, 'honest Injun' on that."

"Fox News Sunday" host Chris Wallace noted that lawmakers from both parties have called that a racial slur.