Democrats have gained the final seat in the battle for the US Senate, sealing their mid-term poll victory in both houses of Congress.
James Webb is a former marine, whose son is serving in Iraq
Republican George Allen admitted defeat to his Democratic opponent, James Webb, in the close Virginia Senate race.
The Democrats had already secured the House of Representatives in Tuesday's elections.
President George W Bush has pledged to work with his rivals, and says he is open to new ideas on Iraq.
He has already accepted the resignation of Defence Secretary Donald Rumsfeld, key architect of US policy in Iraq, following the poll defeat.
The BBC's Adam Brookes in Washington says the loss of both houses of Congress will make Mr Bush's last two years in office extremely difficult.
The Senate victory will also give the Democrats key posts on powerful congressional committees, as well as more control over federal spending.
Levers of power
As a result of their victory, the Democrats will have the right to hold hearings and approve presidential appointments, including those to the Supreme Court.
Our correspondent says the Democrats' win in the Senate will also strengthen the position from which they launch their bid for the presidency in 2008.
The victory in Virginia leaves the Democrats and Republicans with 49 seats each in the Senate.
The remaining two seats are held by independent senators who say they will vote with the Democrats, giving the party a 51-49 majority.
In his speech, Mr Allen said he had telephoned Mr Webb to congratulate him.
He said he did not want to cause "more rancour" by seeking a recount which he did not think would alter the outcome.
Mr Webb had been leading by about 7,000 votes, and although Mr Allen could have demanded a recount, it became clear that further checks were unlikely to overturn the result.
Our correspondent says Mr Allen had been tipped to be a future presidential contender, but his campaign went disastrously wrong.
He was derided in the media for comments which were seen as racist, and appeared to be embarrassed about suggestions that he had Jewish ancestry - while facing a Democratic opponent who was a former marine and strong on national security.
George Allen had been tipped as a future presidential contender
To massive cheers from gathered supporters, Mr Webb held up a pair of boots worn by his son, who is currently serving in Iraq.
He described his opponent as "gracious" and called on President Bush to denounce what he said had been "unnecessarily brutal" tactics in the bitterly fought election campaign.
Earlier, Mr Bush appealed to members of the US Congress to rise above party differences.
"It is our responsibility to put the elections behind us and work together" on the issues facing the US, he said.
He said a lunch on Thursday with Democrat Nancy Pelosi, who is set to become the Speaker of the House of Representatives, had been "very constructive and very friendly".
Ms Pelosi has called for a change of strategy in Iraq, describing the current policy as a "catastrophic path".
Mr Bush said he was open to "any ideas and suggestions" on ways of achieving US goals in Iraq.