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WASHINGTON (CNN) -- Less than an hour after Virginia Republican Sen. George Allen conceded and the U.S. Senate was handed to the Democrats, Jim Webb addressed a cheering crowd.
Before he spoke, Webb waved a pair of combat boots in the air - a campaign trademark for the former Navy secretary whose Marine son is fighting in Iraq.
"We have a much stronger Democratic party...We're going to work hard to bring a sense of responsibility in our foreign policy that will, in my view, result in a diplomatic solution in Iraq," he said.
Webb led Allen by less than 1 percent, or 8,805 votes, Thursday afternoon in the last unsettled race of the 33 Senate contests on Tuesday's ballots, the Virginia State Board of Elections announced.
Allen has offered to help Webb transition to the job and the two will have lunch next week to talk about issues, Webb said.
"I also asked him to help me with something I think is very important, ladies and gentlemen," Webb continued. "And that is that, 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."
Although he could have called for a recount, Allen said he saw "no purpose" in it.
"My friends, sometimes winds -- political or otherwise -- can blow the limbs off branches or break limbs. But a deep-rooted tree will keep growing," Allen said earlier Thursday afternoon from Alexandria, Virginia. His wife, Susan, and young daughter, Brooke, stood by his side.
"The people of Virginia have spoken, and I respect their decision. The Bible teaches us there is a time and place for everything, and today I called and congratulated Jim Webb." (Watch Sen. Allen concede -- 4:29 )
Webb's win marks the first time since May 2001 that the Democrats have snared the 51 votes they need to control the Senate.
The party briefly regained the Senate with the 2001 defection of Vermont Republican Jim Jeffords, only to lose it again in the 2002 midterm election.
A few minutes after Allen's concession, top Democrats gathered near Capital Hill.
Senate Minority Leader Harry Reid of Nevada told a roaring crowd, "The election's over. It's time for a change. It's time for bipartisanship, it's time for open government, transparency, and it's a time for results."
New York Sen. Charles Schumer said, "Will we stand up to the president when we think he is wrong? Yes. But our real mission is to work together and help the American family and make a better America, and we pledge today that we will never lose sight of that, our true mission."
Even before today's concession, Republicans were resigned to facing a Democratic majority next year, one GOP member said Thursday.
"I think if you ask any Republican in Congress right now, they're working under the assumption that they'll be in the minority in both the House and the Senate," Sen. John Sununu of New Hampshire said.
Allen trailed Webb by 8,805 votes Thursday afternoon in the last unsettled race of the 33 Senate contests on Tuesday's ballots, the Virginia State Board of Elections announced.
That margin grew from a roughly 7,200-vote gap Wednesday afternoon after 55 of Virginia's 134 electoral districts completed their canvasses of the results.
Webb declared victory early Wednesday, and The Associated Press declared him the winner Wednesday night.
Webb's win puts the new Senate lineup at 49 Democrats, 49 Republicans and two independents -- Bernie Sanders of Vermont and Joe Lieberman of Connecticut, who have said they would caucus with the Democrats.
Democratic challengers beat five other Republican incumbents in Tuesday's Senate races and won 29 seats in the House to claim control of that chamber for the first time since 1994.
CNN's Dana Bash and Mike Ahlers contributed to this report.
Virginia senator-elect Jim Webb, a former Navy secretary with a son in Iraq, said he will push for a "diplomatic solution" to the war.
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