British Prime Minister David Cameron and Deputy Prime Minister Nick Clegg wave outside 10 Downing Street in London. (Suzanne Plunket/Reuters)

Britain's new prime minister says his Conservative Party and the Liberal Democrats have given their "full backing" to Britain's new coalition government.

"It will be an administration united behind three key principles: freedom, fairness and responsibility," David Cameron said Wednesday.

The two parties approved the alliance on Tuesday after five days of negotiations that followed an inconclusive election in which the Tories won the most seats, but failed to win a majority.

Cameron replaces Gordon Brown as prime minister and Liberal Democrat Leader Nick Clegg has been appointed deputy prime minister. At least four other Liberal Democrat MPs will also serve in cabinet.

Cameron said he will chair the first meeting of a newly created National Security Council on Wednesday afternoon and will work with Clegg to set out the aims and values of the new government in the weeks ahead.

Clegg, left, and Cameron hold their first joint news conference at 10 Downing Street. (Christopher Furlong/Associated Press)

"Until today, we were rivals — and now we're colleagues," Clegg said after Cameron spoke to reporters in the garden at 10 Downing Street.

"That says a lot about the scale of the new politics which is now beginning to unfold."

Clegg said the new government "will last" despite political differences, because the parties share a common purpose.

The coalition has already agreed on a five-year, fixed-term Parliament, which both parties believe will add a measure of stability to the coalition government. It's the first time Britain has had the date of its next election decided in advance.

The two parties are also hoping to work quickly to address Britain's massive budget deficit and soaring unemployment, Cameron said, noting that no government in recent memory had been left with "such a terrible economic inheritance."

The Tories and the third-place Liberal Democrats come from opposite ends of the political spectrum, but the parties have come together to form Britain's first coalition government since the Second World War.

"This is a genuine compromise between the parties," said William Hague, the new foreign secretary.

"There are many things the Liberal Democrats have had to swallow that are very difficult for them, just as there are some things — like holding a referendum on a new voting system — that are very difficult for the Conservative Party to accept."

In an email sent to supporters, Cameron said the agreement allows Conservatives to move forward on school and welfare reform and rejects Liberal Democrat pledges to get rid of nuclear submarines.

The Tories have reportedly agreed, however, to abandon a plan to raise the threshold on inheritance taxes, and they have agreed to let Clegg oversee the national referendum on voting reform.

Labour regroups

Meanwhile, the Labour Party is trying to regroup after dismal election results.

Brown, who resigned as leader of the party, told his supporters that he takes responsibility for Labour's failure to win the election.

"We know more certainly now than ever before that there is a strong progressive majority in Britain," Brown said.

"I wish more than I can possibly say that I could have mobilized that majority to carry that election."

Harriet Harman is serving as interim Labour leader until a formal leadership vote takes place. David Miliband, the former foreign secretary, has emerged as a top candidate and earned the backing of another early favourite, former home secretary Alan Johnson.

The Conservatives won 306 of the 650 seats in the House of Commons. Labour won 258, the Liberal Democrats took 57 and smaller parties won 28, with one seat not yet determined.

With files from The Associated Press