Lib Dem leader Nick Clegg is meeting his MPs and peers to discuss a power-sharing offer from the Conservatives.
The Tories won most votes in the UK election but were short of a majority - Gordon Brown remains PM while Tories see if they can form a government.
Mr Clegg also spoke to the PM by phone on Friday. He has offered talks if Lib Dems cannot agree with the Tories.
Lib Dem negotiator David Laws said MPs and peers backed Mr Clegg's actions and would put "national interest" first.
The three party leaders appeared together at the Cenotaph for VE Day celebrations.
'Endorsed in full'
Mr Clegg has met senior Lib Dem MPs and his wider parliamentary party to sound them out about the options, after the UK election resulted in a hung parliament.
Outside the meeting, Lib Dem negotiator David Laws said the parliamentary party had "endorsed in full" the strategy outlined by Mr Clegg - who said the Conservatives, as the biggest party, had the right to seek to form a government first.
Mr Laws added they were "determined to put the national interest before party advantage" and wanted to "play our part in delivering the stable and good government" that voters expected.
But he did not clarify whether the Lib Dems - the UK's third biggest party - would demand a referendum on changing the voting system as a condition of any deal with the Conservatives.
Protest
An estimated 1,000 people gathered outside the Lib Dem meeting in favour of electoral reform, chanting "Fair votes now". Mr Clegg left the talks briefly to accept their petition, and told them: "Reforming politics is one of the reasons I went into politics."
Mr Clegg will also meet his party's governing body, the federal executive, to discuss Mr Cameron's proposals. He will need the support of a majority of MPs and the executive to enter into any deal.
He has stressed his priorities, including "fundamental political reform", tax reform to make the system fairer, a "new approach" to education to give a "fair start" to all children and to the economy, but said Lib Dems would act in a "constructive spirit" in the "coming hours and days".
Electoral reform is likely to be a key battleground - the Lib Dems have long campaigned for the first-past-the-post system to be replaced with a form of proportional representation. The Conservatives oppose changing the voting system.
The Conservative and Lib Dem negotiation teams will meet again at 1100 BST on Sunday and there will be a meeting of Conservative MPs at 1800 BST on Monday, the BBC understands.
'Progressive' coalition
The approach by the Conservatives has echoes of 1974, when Tory PM Ted Heath spent a weekend trying to agree a coalition with Jeremy Thorpe's Liberal Party. The deal collapsed on the Monday and Mr Heath was forced to resign - leaving Harold Wilson to form a minority Labour government.
Labour frontbencher Peter Hain said it was "clear" that Mr Clegg and Mr Brown had "a lot in common" on the need for electoral reform - Labour has offered a referendum on changing the voting system.
And his colleague Ben Bradshaw told the BBC Gordon Brown - who has gone to his family home in Scotland - could remain prime minister in a "progressive" coalition deal with the Liberal Democrats, if their talks with the Tories failed.
However Labour backbencher John Mann has called for Mr Brown to step down as Labour leader - arguing his position "rules out the credibility of a Lib/Lab pact".
He said: "Gordon Brown has had a good run and whilst he was an excellent chancellor he has been seen as a poor prime minister who is out of touch and aloof. Labour lost votes because of this."
Scotland's First Minister, SNP leader Alex Salmond, called on the Lib Dems to join a "progressive alliance" involving Labour, the SNP and Plaid Cymru - although a Labour source dismissed that as "a desperate attempt by Alex Salmond to make himself look relevant after a terrible general election result".
The Lib Dems have denied suggestions from a senior Lib Dem source of an angry phone conversation between Mr Brown and Mr Clegg. A Lib Dem spokeswoman said it was "perfectly amicable".
Downing Street said it lasted 40 minutes and concentrated on "process".
Voting system
Mr Brown has publicly invited the Lib Dems to talk to Labour, if talks with the Conservatives fail.
The BBC understands some Labour members are already talking to their Lib Dem counterparts to try to persuade them that a deal with the Tories would be a disaster.
Mr Cameron will also face a battle from some Conservatives if he allows senior Lib Dems to serve in a Conservative-led cabinet or bows to demands for change the voting system.
He has offered an "all party committee of inquiry on political and electoral reform" but has not offered a referendum on changing the voting system.
Senior Conservative Liam Fox told the BBC: "It would seem to me very strange in an election that was dominated by the economy...if the government of the UK was held to ransom over an issue that the voters did not see as their priority."
He admitted politicians were "constrained" by the range of views within the party but said the question was whether the parties would focus on their similarities to provide a "stable government for the country" or whether "elements within the parties" would be allowed to focus on their differences.
He said that was not "a free-for-all for politicians cobbling deals after the election".
The Tories secured 306 of the 649 constituencies contested on 6 May. It leaves the party just short of the 326 MPs needed for an outright majority, with the Thirsk and Malton seat - where the election was postponed after the death of a candidate - still to vote.
Labour finished with 258 MPs, down 91, the Lib Dems 57, down five, 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%).
