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David Cameron has reached out to the Liberal Democrats in an effort to form a government – after the UK general election resulted in a hung parliament.
The Tory leader, whose party won most seats but was short of a majority, said he wanted to make a “big open and comprehensive offer” to the Lib Dems.
BBC political editor Nick Robinson said it could include Lib Dems in cabinet.
Labour leader Gordon Brown has already stressed his party’s “common ground” with the third biggest party.
Mr Cameron spoke to his Lib Dem counterpart Nick Clegg by phone on Friday afternoon in what has been described to the BBC as a “very constructive” conversation. However, there was little discussion of details.
Further talks are due on Friday evening, during a meeting involving the Conservatives’ George Osborne, William Hague, Oliver Letwin and Mr Cameron’s chief of staff, Ed Lewellyn. Chris Huhne, Danny Alexander, Andrew Stunnell and David Laws will represent the Lib Dems.
ELECTION 2010: KEY REPORTS
With results from all 649 constituencies contested on 6 May now declared, the Tories have got 306 seats – or 307 including the previously Tory held Thirsk and Malton where the election was postponed after the death of a candidate. It leaves the party just short of the 326 needed for an outright majority.
Labour have finished with 258 MPs, down 91, the Lib Dems 57, down 5, and other parties 28. The Conservatives got 36.1% of votes (up 3.8%), Labour 29.1% (down 6.2%) and the Lib Dems 23% (up 1%).
Past practice under Britain’s unwritten constitution sees the sitting prime minister in a hung parliament having the right to make the first attempt at forming a ruling coalition.
But Mr Cameron said Mr Brown had “lost his mandate to govern” after the Conservatives won the most votes and the most seats.
And Nick Clegg, leader of the third biggest party, the Lib Dems, said he believed the result gave the Tories the right to seek to govern first.
Mr Cameron referred to the “outgoing Labour government” in his speech. But Mr Brown said he was making his statement “as prime minister with a constitutional duty to seek to resolve the situation for the good of the country”.
The Conservative leader said talks would begin with other parties. He said one option was to offer them reassurances about certain policy areas – then try to govern as a minority Conservative government.
But he said it might be possible “to have stronger, more stable, more collaborative government than that”.
“I want to make a big, open and comprehensive offer to the Liberal Democrats. I want us to work together in tackling our country’s big and urgent problems – the debt crisis, our deep social problems and our broken political system,” he said.
While there were policy disagreements between the Tories and Lib Dems – including on the European Union and defence – there were also “many areas of common ground”.
The Conservatives agreed with the Lib Dem on ideas such as a “pupil premium” in schools, a low-carbon economy, tax reform and shared opposition to Labour’s ID cards scheme.
But he did not pledge a referendum on changing the voting system – a key concern of the Lib Dems – instead offering an “all party committee of inquiry on political and electoral reform”.
“I think we have a strong basis for a strong government. Inevitably the negotiations we’re about to start will involve compromise. That is what working together in the national interest means,” Mr Cameron said.
BBC political editor Nick Robinson said Mr Cameron had not ruled out a coalition, with places for Liberal Democrats in a Conservative-led government.
But he said while he doubted the Lib Dems would take them up on the offer, they might be prepared to let Mr Cameron govern by not voting down the Queen’s Speech or Budget. Taking that option would allow them not to be tainted by decisions they did not like.
However former Conservative prime minister Sir John Major told the BBC offering the Lib Dems cabinet seats was “a price, in the national interest, that I personally would be prepared to bear” for the formation of a stable government able to manage the economic crisis.
Earlier, outside No 10, Mr Brown said he would be “willing to see any of the party leaders” adding: “I understand and completely respect the position of Mr Clegg in stating that he wishes first to make contact with the leader of the Conservative Party.”
But he added “should the discussions between Mr Cameron and Mr Clegg come to nothing… I would be prepared to discuss with Mr Clegg the areas where there may be some measure of agreement between our two parties”.
He said there were areas of “substantial common ground” – including reforming the voting system and plans to ensure economic stability, he said.
He also said he did not expect a swift conclusion to the uncertainty surrounding the election result – saying the voters had given their verdict and it was now “our responsibility now to make it work for the national good”.
BBC political correspondent Iain Watson said Mr Brown’s message was directed at Lib Dem supporters – spelling out what a Labour government would offer them in the hope of getting them to put pressure on Mr Clegg not to do a deal with the Conservatives.
Mr Clegg – whose party has done worse than in 2005 despite favourable opinion polls – said that he believed the Tories had gained the “first right” to attempt to form a government in the “national interest”.
Speaking outside Lib Dem headquarters in London, he said: “It is vital that all parties, all political leaders, act in the national interest and not out of narrow party political advantage.”
He also admitted it had been a “disappointing night” for the Lib Dems.
Downing Street has authorised the civil service to support other parties in hung parliament negotiations – essentially giving the go-ahead for talks to begin.
In other election night news:
Northern Ireland’s first minister and DUP leader Peter Robinson has been defeated in East Belfast by the Alliance party
The Greens gained their first MP at Westminster – party leader Caroline Lucas in Brighton Pavillion
Education secretary Ed Balls hung on in Morley and Outwood by just over 1,000 votes but former Home Secretary Charles Clarke narrowly lost to the Lib Dem candidate in Norwich South
Jacqui Smith, who stood down as home secretary over her expenses, lost her Redditch seat to the Conservatives but Hazel Blears retained her seat in Salford
Labour’s Margaret Hodge beat the BNP’s Nick Griffin in Barking and Dagenham, with a 5% increase in her vote
Esther Rantzen came fourth in Luton South, which went to the Labour candidate
Lib Dem frontbencher Lembit Opik lost his Montgomeryshire seat after suffering a 13.2% swing to the Conservatives
Scotland’s First Minister Alex Salmond rules out an SNP deal with the Conservatives but their “Celtic bloc” partners in Wales, Plaid Cymru, leave the door open to a deal
An inquiry has been promised after people were turned away from polling stations as long queues formed ahead of the 2200 BST voting deadline.