The Conservatives have made a "final offer" to the Lib Dems of a referendum on electoral reform as the battle to form the UK's next government heats up.
Tory deputy leader William Hague said he would offer Nick Clegg's party a vote on the Alternative Vote system.
It comes after Gordon Brown, who said he was standing down as Labour leader, offered to put AV into law with a referendum for voters to approve it.
The Lib Dems must now decide which party they want to back.
Speaking outside the House of Commons, Mr Hague urged the Lib Dems to accept the Tory deal, arguing that to join with Labour would mean "a second unelected prime minister in a row" and the imposition of voting reform without first consulting the public in a referendum.
This was later denied by Labour sources, who said they would pass a law on AV immediately, but then hold a referendum to allow voters to approve or reject it. There were also unconfirmed reports Labour was offering the prospect of full proportional representation at a later stage.
Mr Hague said a deal with the Tories was the only way to guarantee the "strong, stable government" the Lib Dems say they want, as it would give the two parties a "secure Parliamentary majority of 76".
Labour would have to band together with other parties such as the Scottish Nationalists, Plaid Cymru, the Green Party and the SDLP in order to guarantee a working majority.
The Conservatives are also understood to be offering the Lib Dems fixed-term Parliaments.
Mr Hague said the focus of Conservative negotiations with the Lib Dems, which have been going on for three days since the general election ended with no clear winner, has been on the economy.
The Conservatives have long been opposed to a referendum on electoral reform but in his statement Mr Hague said: "In the interests of trying to create a stable, secure government we will go the extra mile and we will offer to the Liberal Democrats, in a coalition government, the holding of a referendum on the Alternative Vote system, so that the people of this country can decide."
Mr Hague warned it would be a "great mistake" for the Lib Dems to do a deal with Labour given their "apparent attachment to improving democracy".
He said: "It would be wrong to construct a government, which wouldn't be stable, which wouldn't have a prime minister elected by the people of this country and wouldn't be submitting a major constitutional change to a referendum of the country."
Mr Hague said that in a possible referendum, Conservative MPs opposed to change in the voting system would be "at liberty" to campaign against it.
Shadow chancellor George Osborne said a weak coalition struggling to achieve a Parliamentary majority was "not in the national interest".
"The Liberal Democrats want to change our voting system and we are making that offer.
"So the parliamentary party, in the extraordinary meeting where we genuinely consulted them following a meeting of the shadow cabinet, has pretty much to a person - I can't think of a single person who objected - endorsed the position set out and agrees to make this offer now to the Liberal Democrats as a final offer."
Conservative sources have told the BBC that on Monday morning the Conservative and Liberal Democrat teams were discussing a stripped-down deal in which the Lib Dems would not topple the Tories in a confidence vote.
It is now understood the Lib Dems are seeking a full coalition with either Labour or the Conservatives.
There are no plans at the moment for Tory negotiators to resume their talks with the Lib Dems, the BBC understands.