Liberal Democrat leader Nick Clegg held talks with his party's lawmakers on Saturday to plan their strategy as he considers a power-sharing deal with the Conservatives to solve the political impasse.
The Liberal Democrats are responding to David Cameron's "big, comprehensive offer" after Thursday's landmark general election resulted in the first hung parliament for 36 years.
The Conservatives won the most seats but failed to secure the overall majority which would have allowed them to govern alone after a 13-year absence and immediately remove Labour Party from power.
With Brown still in the prime minister's residence in Downing Street, Conservative and Liberal Democrat negotiators held a first meeting on Friday evening and Clegg and Cameron spoke on the telephone.
A Lib Dem spokesman said: "They agreed that they should explore further proposals for a programme of economic and political reform."
The Conservatives would like to finalise a power-sharing deal before the financial markets open on Monday, but Clegg does not want to be hastily forced into anything he cannot sell to party members who must approve any deal.
The parties are not natural political partners, with the Lib Dems closer to Labour in many areas.
The key points of divergence between the two are the Lib Dems' commitment to electoral reform to introduce proportional representation, the future of the Trident nuclear deterrent and Britain's role in Europe.
In making his offer on Friday, Cameron insisted there was common ground but only proposed setting up an all-party inquiry into electoral reform, a proposal likely to fall short of the demands of the Lib Dem rank-and-file.
Senior Lib Dem lawmaker Simon Hughes told BBC radio that negotiations with the Conservatives could continue for many days: "We are all working constructively. Talks will go on over the weekend," he said.
He said there would be no formal coalition offer on the table for the Lib Dem lawmakers to consider on Saturday. "There won't be a deal on the table because the talks have only just begun, but we will discuss where we want to go.
"When the talks have gone as far as they can there will have to be a view taken," he said.
But the Conservatives' defence spokesman Liam Fox warned the talks could not be "held to ransom" by the Lib Dems demanding proportional representation.
He stressed that the Tories had won the most seats and the most votes and had made it clear in the campaign that "we were very much against it (proportional representation)".
"What leaders will have to focus on is the fact that the Conservatives are the biggest party and it's reasonable that a programme would be followed that put the larger part of our manifesto into place," he told BBC radio.
If a deal cannot be done, Cameron made clear he was also prepared to try to rule as a minority Conservative government relying on support from smaller parties.
The Conservatives have 306 lawmakers in the 650-seat House of Commons, compared to 258 for Labour and 57 for the Liberal Democrats.
Unionist parties in Northern Ireland, who won eight seats, could play a key role in backing a minority government.
Brown and Labour are waiting in the wings if the Lib Dems and the Conservatives cannot force through a deal.
Brown, while saying he respected Clegg's decision to talk to the Tories first, said he too was open to negotiation with the Lib Dems and tried to entice them with the prospect of immediate legislation on electoral reform.
Power-sharing governments are so unusual in the House of Commons that some commentators said a fresh election might be the only route to a solid government.
The pound slumped to a 13-month low against the dollar and London stocks sank on fears the deadlock would hamper the nation's ability to slash the giant public debt.
The press said a deal to create a stable government was needed fast.
The Financial Times said a Tory-Lib Dem pact offered the best hope of stability because it was the only plausible combination.
The Daily Telegraph said Britain needed a new government in place before Monday to prevent turbulence in the financial markets.
Source: AFP European Edition