Talks between the Liberal Democrats and the Conservatives at the Cabinet Office on Sunday were "positive and productive", William Hague said.
The shadow foreign secretary made the statement after emerging from the meeting, which lasted nearly seven hours.
"We've had some very positive and productive discussions over many key policy areas," he said.
"We intend to meet again over the next 24 hours."
The two parties discussed political reform, deficit reduction, banking reform, civil liberties and environmental issues.
Davis Cameron and NickClegg had a private meeting this evening for approximately 40 minutes.
Danny Alexander, Nick Clegg's chief of staff, said they had had "good discussions on a wide range of issues".
David Cameron and Mr Clegg did not attend the meeting, but the two men talked on the phone earlier today. More talks will take place in the next 24 hours.
Mr Clegg and Gordon Brown also met today, in the Foreign Office, according to media reports.
David Cameron has gone to Portcullis House, where he will be meeting new and old MPs.
He will meet with his parliamentary party tomorrow evening. Labour is reported to be organising a national executive meeting on Tuesday night.
Several key Cabinet ministers arrived in Downing Street for what appeared to be a high-level meeting today, not long before Mr Brown is reported to have had his meeting with Mr Clegg.
All parties are succeeding in maintaining a high level of silence around the negotiations, with very few briefings or leaks taking place. The details of the negotiations have been kept firmly under wraps.
Mr Cameron and Mr Clegg last met on Saturday evening in talks described as "constructive and amicable". It was reported this morning that Mr Clegg also talked with Gordon Brown over the phone last night.
Despite indications of clear progress being made, the negotiations remain in their early stages. It is understood the parties are seeking consensus on areas of agreement before tackling more divisive issues.
Mr Clegg reiterated his support for electoral reform, the real point of contention in negotiations, as he emerged from talks with Lib Dem MPs in central London to address a crowd of around 1,000 Unlock Democracy protestors yesterday.
Mr Cameron faces pressure from his party not to concede the referendum in a shift away from the first-past-the-post system.
Disquiet among many of his new backbenchers could come to a head in the first meeting of Tory MPs set to take place on Monday evening. Many are deeply concerned senior Tories could lose sight of the bigger picture in a bid to secure Lib Dem support.
One new Conservative MP told politics.co.uk that most members of the new House of Commons would be "very wary of a major shift towards proportional representation".
The public appear determined to secure a change from the current system. An ICM survey for the Sunday Telegraph newspaper found 48% of the public favoured the introduction of proportional representation, which would make hung parliaments the norm.
In an email to supporters this morning, Mr Brown said: "My duty as prime minister has been to seek to resolve this situation but I also have another important role as leader of the Labour party.
"My resolve has not, and will not, change."
A poll for the Sunday Times by YouGov found a majority of people disapproving of Mr Brown's refusal to resign as leader after he failed to secure a fourth term for New Labour.
Rumours that Labour MPs with links to the Liberals, including former members of the SDP, are courting their potential progressive allies are not being officially sanctioned - but politics.co.uk understands they are taking place.
"I'm sure people who are friends in different parties speak to each other," a Labour party spokesman said yesterday.
Mr Brown is constitutionally permitted to remain the prime minister until it becomes clear he can no longer command a majority in the Commons. His behaviour mirrors that of Ted Heath in 1974 - who remained in Downing Street until the Monday evening after polling day.
Not all Labour campaigners believe the best course for Labour is a coalition with the Liberal Democrats, however.
Francis Steer, the agent for Luton South's newly-elected MP Gavin Shuker, told politics.co.uk he viewed this as the "worst scenario" possible.
"I think the best scenario for the Lab party is a Tory-Lib Dem coalition which I guess wouldn't last very long," he suggested.