Challenger Jim Webb tipped the Senate scale to a Democratic majority Thursday, declaring victory two days after American voters went to the polls in Virginia, home to one of the closest races of the election season.

"I'm walking into the United States Senate with the independence to represent the people who have no voice in the corridors of power, and I intend to do that," Webb told supporters in Arlington, Va.

The former Navy secretary under President Reagan said he joined the Democratic Party because he was concerned not just about the war in Iraq, but economic and social issues.

"I think I and a lot of people like me had aligned themselves with the Republican Party on national security issues but were always concerned about issues of economic fairness and social justice," he said of his party conversion. "This was a very natural fit for not only myself, but for a lot of people who came forward and supported this campaign who, in the past, may not have been inclined to. We have a much, much stronger Democratic Party as a result of this."

Virginia Republican Sen. George Allen conceded the race at 3:15 p.m. ET during a press conference in Alexandria, Va.

"Sometimes winds, political or otherwise, can blow the leaves off branches or even break limbs but a deep-rooted tree will stand. Stay standing. It will regrow in the next season," Allen said.

In this season, the people of Virginia, who I also call the owners of the government -- they have spoken, and I respect their decision," he said. "The Bible teaches us that there's a time and place for everything and today, I've called and congratulated Jim Webb and his team for their victory."

The Virginia Board of Elections previously had announced it would not certify the outcome of the race between Allen and Webb until Nov. 27, after which a requested recount could begin. The candidates were separated by about 7,200 votes out of more than 2.3 million cast, with indications from both camps that any final outcome could wind up in court.

Allen, however, said he would not ask for a recount.

"It is with deep respect for the people of Virginia and to bind factions together for a positive purpose that I do not wish to cause more rancor by protracted litigation which would, in my judgment, not alter the results," Allen said.

"I see no good purpose being served by continuing and needlessly expending money and causing anymore personal animosity. Rather than bitterness ... I want to focus on how best Virginia can be effectively served by their new junior senator."

Webb told supporters his GOP rival was "very gracious" in his concession phone call and that he offered to assist the incoming senator during the transition period.

"I thanked him for his many years of service in Virginia," Webb said. He and Allen are having lunch next week.

But Webb said he also asked for Allen's help on another issue.

"As we move forward with all of these issues that concern us as Americans, I think it's really vital that we all do our best to stop the politics of divisiveness, character assassination, distraction," said Webb, whose campaign was one of the more polarizing in the country.

"I would like to also today call on our president to publicly denounce the campaign tactics that have divided us rather than brought us together. This was a brutal campaign and in many ways, a unnecessarily brutal campaign and I think it's hurting the country."

Allen was the last of six GOP incumbents to lose re-election bids in a midterm election marked by deep dissatisfaction with President Bush and the situation in Iraq.

GOP Sen. Conrad Burns earlier Thursday conceded the Senate race in Montana to Jon Tester. That move, along with Allen's concession, gave Democrats control of 49 seats in the Senate -- with two independents caucusing with the Democrats -- and a full sweep of Congress.

Burns caught Tester on the phone as he headed for a barbershop to get his famous flattop style trimmed.

The call was "very cordial, very professional. It was positive," Tester, a farmer and state legislator, told The Associated Press.

Burns, a three-term GOP senator whose campaign was troubled by gaffes and voter discontent, did not plan any public appearances Thursday. But he released a written statement saying he was ready to "help as Montana transitions to a new United States Senator."

"We fought the good fight and we came up just a bit short. We've had a good 18 years and I am proud of my record," he said.

After 12 years of near-domination by the Republican Party, the shift dramatically alters the government's balance of power, leaving Bush without GOP congressional control to drive his legislative agenda. Democrats hailed the results and issued calls for bipartisanship even as they vowed to investigate administration policies and decisions.

Democrats won 234 seats in the House, considerably more than the 218 necessary to hold the majority in the 435-member chamber.

"In Iraq and here at home, Americans have made clear they are tired of the failures of the last six years," said Sen. Harry Reid of Nevada, in line to become Senate majority leader when Congress reconvenes in January.

As watershed elections go, this one rivaled the GOP's takeover in 1994, which made Newt Gingrich speaker of the House, the first Republican to run the House since the Eisenhower administration. This time the shift comes in the midst of an unpopular war, a Congress scarred by scandal and just two years from a wide-open presidential contest.

Democrats will have nine new senators on their side of the aisle as a result of Tuesday's balloting. Six of them defeated sitting Republican senators from Pennsylvania, Ohio, Missouri, Rhode Island, Montana and Virginia. The other three replaced retiring senators from Maryland, Minnesota and Vermont.

Their ideologies are as varied as their home states. Bernie Sanders, an independent who will replace retiring Vermont Sen. Jim Jeffords, is a socialist who has served in the House and voted with Democrats since 1990. Bob Casey Jr., who defeated Republican Sen. Rick Santorum in Pennsylvania, is an anti-abortion moderate. Webb once declared that the sight of President Clinton returning a Marine's salute infuriated him.

In the House, five races remained too tight to call, but the margin offers little room for achievements if bitterness remains. Rep. Nancy Pelosi, the putative House speaker, called for harmony and said Democrats would not abuse their new status.

She said she would be "the speaker of the House, not the speaker of the Democrats." Democrats would aggressively conduct oversight of the administration, but said any talk of impeachment of President Bush "is off the table," she said.

In the Senate, Sen. Charles Schumer of New York, the head of the Democratic Senatorial Campaign Committee, said, "We had a tough and partisan election, but the American people and every Democratic senator — and I've spoken to just about all of them — want to work with the president in a bipartisan way."

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Despite the "thumpin'" Bush said Republicans took in the House and the possibility of also losing control of the Senate, Bush has vowed to reach out to Democrats to show the American people that things can get done, no matter the makeup of the legislative and executive branch.

"I told my party's leaders that it is now our duty to put the elections behind us and work together with the Democrats and independents on the great issues facing this country," he said.

Pelosi is set to become the first female speaker of the House. Rep. Steny Hoyer of Maryland and John Murtha of Pennsylvania announced they will run for the majority leader post, the second in command in the House.

Extending an olive branch, the president invited Democratic leaders to the White House to talk about the agenda for next year. Pelosi and Hoyer joined the president for lunch on Thursday to strategize on how they can work with Bush in the coming legislative sessions. Reid and Sen. Dick Durbin of Illinois are scheduled to go to the White House on Friday.

FOX News' Carl Cameron and The Associated Press contributed to this report.