The three leaders all attended VE Day celebrations at the Cenotaph
The Lib Dem leadership has "endorsed in full" Nick Clegg's decision to talk to the Tories first - after the UK election resulted in a hung parliament.
The Tories won most votes but were short of a majority and have asked for Lib Dem support to form a government.
David Cameron met Mr Clegg privately for the first time to discuss the progress of the parties' negotiations.
Gordon Brown who remains PM spoke to Mr Clegg by phone. He has offered the Lib Dems talks if no deal is reached.
Mr Clegg has been discussing the Tory power-sharing offer with his party.
After a meeting of Lib Dem MPs and peers, 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.
BBC political editor Nick Robinson said the talks between Mr Cameron and Mr Clegg followed an earlier brief conversation at the VE day commemoration in London.
Both parties described the 70 minutes long meeting, which took place at Admiralty House in Westminster, as "constructive and amicable".
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.
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.
He said talks had been "very positive and constructive" but 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.
An arrangement between Labour, the Lib Dems, the SNP and Plaid could command a majority in the House of Commons. The nationalist parties would, of course, extract financial and political concessions
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 has also met his party's governing body, the federal executive, to discuss Mr Cameron's proposals. The federal executive said they also endorsed the Conservatives' right to seek to form a government first.
Mr Clegg needs the support of a majority of Lib Dem 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 three party leaders appeared together on Saturday at the Cenotaph for VE Day celebrations.
David Laws: "We are keen for an early conclusion to these issues"
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 before the party conference in September - 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."
It would seem to me very strange... if the government of the UK was held to ransom over an issue that the voters did not see as their priority
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.
However 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".
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 in the voting system.
In a message emailed to party supporters on Saturday evening he said he would stand firm on his pledges not "to give more powers to Brussels, be weak on immigration or put the country's defences at risk".
But he said areas of common ground with the Lib Dems included "the need for education reform, building a low-carbon economy, reforming our political system, decentralising power, protecting civil liberties and scrapping ID cards".
And he said in the "national interest" the Conservative Party may be able to give ground in areas such as the Lib Dem manifesto plan to reduce taxes on the lowest paid, adding: "Of course, we hope to see a similarly constructive approach from the Liberal Democrats - not least on the urgent issue of tackling the deficit."
He said: "I hope we can sort things out as quickly as possible, for the good of the country. But we won't rush into any agreement."
There was no direct reference to the Lib Dem desire for a referendum on voting reform although on Friday he offered an "all party committee of inquiry on political and electoral reform".
Meanwhile, a YouGov poll for the Sunday Times suggests more than two-thirds of people want Mr Brown to leave Downing Street immediately.
The poll of more than 1,400 voters found people think he should have conceded defeat on Friday, rather than hanging on in case the Conservatives cannot come to a deal with the Liberal Democrats.
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%).
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