Prime Minister Gordon Brown has made a direct overture to Liberal Democrat leader Nick Clegg, offering immediate legislation on a referendum on electoral reform in return for a deal which could keep him in Downing Street.
Speaking on the steps of No 10, Mr Brown said he believed discussions on a "fairer voting system" were "essential" and he underlined his commitment to putting proposals for reform to the country in a referendum.
But while he said that Mr Clegg and Mr Cameron, the Tory leader, should have as much time as they needed to complete their discussion, he stressed that all the parties had a responsibility to make the outcome of the election "work for the national
Mr Brown said: "What all of us need to be mindful of is the imperative for a strong and stable government and for that to be formed with the authority to tackle the challenges ahead and one which can command support in Parliament.
"It is with this in mind that all of us should be facing the times ahead.
"I understand - as I know my fellow party leaders do - that people don't like the uncertainty or want it to be prolonged.
"We live, however, in a parliamentary democracy. The outcome has been delivered by the electorate. It is our responsibility now to make it work for the national good."
Mr Brown said voters had sent "a very strong message which must be heard" on the need for electoral reform and said immediate legislation was needed to restore public trust in politics.
He left no doubt that he has no intention of resigning immediately as Prime Minister, even talking of his plans to stabilise the economy beyond the end of 2010.
And he said Mr Cameron and Mr Clegg should be given "as much time as they feel necessary" to sound out whether a deal between them is possible.
"Clearly, should the discussions between them come to nothing, then I would, of course, be prepared to discuss with Mr Clegg the areas where there may be measures of agreement between our two parties," he added.
Mr Cameron will this afternoon make a public statement setting out how he will seek to form "a Government that is strong and stable with broad support, that acts in the national interest" in what is expected to be a direct challenge to Mr Brown to concede defeat.
Yesterday's election left the Conservatives as the largest single party in the new House of Commons, but short of the 326 MPs needed for an outright majority in the UK's first hung Parliament since 1974.
Mr Clegg this morning offered him the keys to 10 Downing Street, saying that - as the party with the most seats and the most votes - the Conservatives had the "first right" to seek to form a government.
Mr Clegg made clear that he was ready to enter talks over a possible deal, saying it was now for the Conservative Party "to prove that it is capable of seeking to govern in the national interest".
In a statement on the steps of the Liberal Democrats' Westminster HQ, Mr Clegg announced: "I have said that whichever party gets the most votes and the most seats has the first right to seek to govern, either on its own or by reaching out to other parties and I stick to that view."
But it was thought far from certain that Mr Cameron will accept any deal with the Lib Dems which includes reform of Westminster's first-past-the-post voting system.
The Tory leader - who was expected to hold a conference call with his Shadow Cabinet before this afternoon's statement - may seek to govern at the head of a minority administration with support from Northern Irish unionists, rather than offer the electoral reform that is likely to be an essential condition of any deal with the Lib Dems.
With 16 seats to declare, the Conservatives had secured 299 MPs, with Labour on 254 and the Liberal Democrats on 54. The Tories were likely to finish with a 36% share of the vote, with Labour on 29% and the Lib Dems 23%.
The projected results indicated that a Conservative/Lib Dem coalition could provide a solid overall majority in the Commons, but that if Labour was to enter into a deal with Mr Clegg, they would also require the support of smaller parties like the Welsh and Scottish nationalists, the SDLP and Britain's first Green MP.
The pound tumbled against the dollar and euro and the FTSE 100 index fell to a three-year low today as the markets took fright at the prospect of a hung Parliament.
Mr Brown this morning fired the starting pistol on haggling over the future government which could last days, when he ordered the head of the Civil Service, Cabinet Secretary Sir Gus O'Donnell, to provide official support for discussions between the parties.
Scottish National Party leader Alex Salmond revealed that his party and Welsh nationalists Plaid Cymru have accepted an offer from the Prime Minister to discuss possibilities for future government.
Speaking to the BBC, he explicitly ruled out a deal with the Tories but added: "Fate seems to have dealt us a mighty hand between ourselves and Plaid Cymru.
"I'm accepting the offer of the Prime Minister, on behalf of the SNP, and Plaid Cymru are accepting, to have the Civil Service back-up to have discussions to see what the possibilities are in terms of defending the interests of Scotland and Wales in this parliamentary situation."
Mr Brown said he was addressing the country as Prime Minister in a "position unknown to this generation of political leaders".
He said he now had a constitutional duty to seek to resolve the situation for the good of the country.
"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," he said.
"Mr Cameron and Mr Clegg should clearly be entitled to take as much time as they feel necessary.
For my part, I should make clear that I would be willing to see any of the party leaders.
"Clearly if the discussions between Mr Cameron and Mr Clegg come to nothing, then I would of course be prepared to discuss with Mr Clegg the areas where there may be some measure of agreement between our two parties."