By Ian Dunt
Nick Clegg and David Cameron have met to try to trash out the terms of a Lib Dem-Conservative coalition.
The two men met fro around 70 minutes in Admiralty House in Westminster. Both parties described the meeting as "constructive and amicable".
In an email to supporters, Mr Cameron said: "Inevitably, these negotiations will involve compromise. But that's what working together in the national interest means.
"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.
The Liberal Democrats and Conservatives will continue talks at the Cabinet Office tomorrow after Mr Clegg took Mr Cameron's offer of coalition government to his own party.
Mr Clegg met his front bench team to discuss the Tory offer this morning. At midday a long meeting began with the parliament party - the Lib Dems' new and old MPs.
David Laws, a member of the frontbench team, said the party had backed Mr Clegg's strategy.
"We will continue to put the national interest first and play a constructive role in providing the stable and good government people deserve," he said.
"We have heard what the Labour party and Gordon Brown are saying but in line with the position Nick Clegg outlined yesterday we are continuing discussions with the Conservative Party as the party with the most seats and votes..
"We want to complete this process as soon as possible but people will recognise that it is also important to get these decisions right in the long term national interest."
The pressure is on the parties, not for constitutional reasons but because of continued worries over jitters in the markets.
With the Greek crisis increasingly spreading to Portugal and Spain, the markets are showing signs of returning to panicky behaviour, putting the pressure on political negotiators to secure a deal quickly in a bid to calm nerves.
Speaking just before a meeting with his frontbench team this morning, Mr Clegg said: "Clearly the result of the election means politicians have the duty to speak to each other.
"I'm very keen to enter into any discussion with other parties as we're doing in a constructive spirit as we're doing in the next few days."
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.
The BBC reported that an angry exchange had taken place yesterday between Mr Clegg and Gordon Brown, in which the Lib Dem leader suggested the prime minister should step down. At that point, according to one Lib Dem source, Mr Brown shouted at Mr Clegg in a "lengthy diatribe". Labour and Lib Dem sources later denied this, saying the conversation was constructive.
The three party leaders put the ongoing talks to one side today when they met at the VE day celebrations.
Meetings last night saw the Lib Dems and Tories suggest to reporters that things were progressing "properly".
Leaving the meeting late last night, shadow foreign secretary William Hague said: "We've had an initial meeting. That's all there is to say at the moment."
Lib Dem energy spokesman Simon Hughes said: "Things are going properly. Things are going carefully. I am not going to speculate. You'll just have to wait."
The meeting followed an open statement from Lib Dem leader Clegg yesterday in which he reiterated his opinion, expressed on several occasions during the election campaign, that the party with the most seats and votes in a hung parliament had the right to be first to try to form a collation with the Lib Dems.
David Cameron reciprocated with a "big, open and comprehensive offer" to Mr Clegg, although the Tory leader's red lines were many; including defence, immigration, Europe and the deficit. Mr Cameron also offered only an all-party inquiry into electoral reform - one of the Lib Dems' red lines - but not a referendum.
Mr Clegg is severely restricted on how he can negotiate due to the Lib Dems' 'triple-lock' system, which limits the leader's room for manoeuvre by checks from MPs, the executive and party members.
On the Conservative side, Mr Hague forms the heart of the Tory team, surrounded by shadow chancellor George Osborne, Oliver Letwin and Mr Cameron's chief of staff Ed Lewellyn.
The Lib Dem negotiation team consists home affairs spokesman Chris Huhne, Andrew Stunnel, David Laws and Mr Clegg's chief of staff, Danny Alexander.
The Conservatives will hold a meeting of the parliamentary party on Monday evening.
Meanwhile, the Scottish National party (SNP) and Plaid Cymru made the opening moves in a bid to create a 'progressive coalition' today.
Both parties appointed teams to discuss the mechanics of any future discussions with their dedicated UK liaison officials in London.
With major benefits to be gained for both parties from any move towards PR, Labour may be interested in securing an informal agreement with the nationalists so they could instantly make up the numbers necessary for a majority should Mr Clegg decide to reject the Conservatives.