The decision closed a rancorous session in which Republicans first sought to push Bolton through the Foreign Relations Committee and Democrats resisted.
"We'll all have to trust each other," said Sen. Richard Lugar, R-Ind., the committee chairman, in sealing the unanimous agreement.
Republicans hold a 10-8 majority on the panel, and Lugar had sounded confident early in the session that he had the votes to prevail.
But Republican Sens. Chuck Hagel of Nebraska and George Voinovich of Ohio, both expressed reservations about a quick vote — as did a solid phalanx of Democrats.
"Although the committee began with the chairman, Senator Richard Lugar saying that the vote was clear on the committee, the only thing clear at the close of the session was that allegations were becoming more numerous and the old adage, 'It's not over until it's over,' was the rule of the day," reports CBS Foreign Affairs Analyst Pamela Falk.
Bolton is a harsh critic of the United Nations bureaucracy and thus was a provocative choice to be the administration's representative to the world body.
That was enough to generate some Democratic opposition, and his troubles were compounded by allegations about his temperament and his ways of dealing with subordinates.
President Bush has no second thoughts about Bolton as his choice to be United Nations ambassador, the White House said Tuesday, despite critics' complaints about Bolton's treatment of subordinates and dismissive comments on the U.N.
Asked if the president had any reservations about Bolton's fitness for the post, White House press secretary Scott McClellan replied: "Absolutely not."
Bolton has addressed all questions about his record and behavior by testifying before the committee and offering additional answers to the panel in writing, McClellan said.
Several Republicans have made it clear they have reservations, that the president could have chosen someone better for the post, but it would be extraordinary for a Republican to vote against one of the Mr. Bush's nominees, reports CBS News Capitol Hill Correspondent Bob Fuss.
At least one Democratic senator, Sen. Christopher J. Dodd, D-Conn., said he would ask for a closed session so the committee could hear from intelligence officials about information Bolton requested relating to National Security Agency communications.
According to a spokesman for Dodd, Bolton asked for and received the identities of 10 U.S. officials involved in such secret NSA interceptions during the past four years.
Democrats also wanted more information about Bolton's dealings with a female employee during his time at the Justice Department in the late 1980s. The two clashed over the woman's request for extended maternity leave.
Bolton is a harsh critic of the United Nations bureaucracy and thus a provocative choice to be Washington's representative to the world body. Most of the allegations that have accompanied his nomination, however, concern his personal dealings and judgment.
The allegations attempted to paint Bolton as an imperious hothead who dressed down junior bureaucrats and withheld information from his superiors in his current job as the State Department's arms control chief.
There were repeated questions by senators at his confirmation hearing last week concerning what Bolton may have done to punish or pressure underlings who crossed him. A senior colleague called him a "serial abuser."
Bolton denied he did anything improper, but said he had "lost confidence" in two intelligence analysts who disagreed with him.
Bolton, 56, has served four years as arms control chief at the State Department, but he is not a diplomat by training. He was an assistant attorney general in the Justice Department under Bush's father, President George H.W. Bush, and held other government jobs during the Reagan administration.
A Yale Law School graduate, Bolton has been a lawyer in private practice and an academic.
He is considered one of Mr. Bush's most conservative advisers on foreign policy, and one of the most caustic.
He has said, for example, that the loss of 10 stories from the United Nations headquarters building in New York would make no difference.
When the State Department was trying to move toward accommodation with North Korea over its nuclear program two years ago, Bolton called the country's leader, Kim Jong Il, a "tyrannical dictator."