LONDON – Britain went for a second day Saturday without a new government as the main parties haggled over possible power-sharing arrangements in a divided Parliament.

All eyes were on the Liberal Democrats, the smaller party that holds the balance of power after neither of the “big two,” Labor and the Conservatives, was able to achieve a majority of seats in the House of Commons in Thursday’s general election.

The Liberal Democrats’ leader, Nick Clegg, met Saturday with senior party representatives and newly elected members of Parliament to discuss an invitation by the Tories, as the Conservatives are known, to join them in some sort of coalition.

Clegg, who gained prominence after a telegenic turn in Britain’s first national debates, has said the Conservatives deserve the first chance of putting together a government after having won the most seats by far.

But there was no sign that a quick deal between the two parties was in the offing despite a meeting Saturday evening between Clegg and David Cameron, the Tory leader. Cameron has urged swift action to calm financial markets worried by the inconclusive election result.

Negotiators for the two parties were scheduled to meet for a second time today. Analysts said the bargaining looked set to drag on through Monday.

“We are keen for an early conclusion to these issues, but people will also understand that we are keen to make sure that we make the right long-term decisions for the people of this country,” said David Laws, one of the Liberal Democrats’ negotiators.

In talking with the Tories, Clegg and his party face a difficult choice that could come down to power vs. principles.

An article of faith for the Liberal Democrats is revision of Britain’s electoral system, which reinforces the two-party lock on politics. The system rewards the winning of parliamentary seats, so clumped-up support in individual voting districts ultimately carries more weight than evenly distributed support across the nation.

The distorted effects of that were on display Thursday when the Liberal Democrats captured 23 percent of votes nationally but were able to win less than 9 percent of the seats in Parliament.

But the Conservatives oppose any change to the system, and Cameron promised only that he would set up a multiparty committee to look into various options.

The danger for Clegg of compromising on the issue was made in noisy fashion by hundreds of protesters who gathered outside the party meeting in London. Warning those inside not to “sell out,” the demonstrators presented Clegg with a petition for electoral change after the meeting.

“Take it from me: Reforming politics is one of the reasons I went into politics,” Clegg told the crowd when he emerged from the meeting. “I genuinely believe it is in the national interest for us to use this opportunity to usher in a new politics after the discredited politics of the past.”

Other differences remain with the Tories on matters of defense, immigration and the key question of how to reduce Britain’s ballooning budget deficit. The Conservatives advocate an immediate program of $9 billion in spending cuts; the Liberal Democrats favor a more cautious approach.

Many Liberal Democrats harbor an instinctive loathing of the Conservative Party, but the temptations of power could prove strong, especially if the Tories agree to a coalition that would award Cabinet posts to Clegg and one or two of his senior colleagues. None of the Liberal Democrats in Parliament has ever tasted life inside government; the party has always looked glumly on from the sidelines as Labor and Conservative took turns ruling the country.

Although the focus is on whether the Liberal Democrats and the Tories can hash out an agreement, Labor Party leaders kept up their own campaign to woo the new kingmaker.

While Prime Minister Gordon Brown mostly holed up in 10 Downing St., the official residence many think he will soon vacate, his deputies reiterated his proposal to hold a referendum on electoral change.

“Nick Clegg and Gordon Brown have a lot in common on the need for fundamental, radical political reform,” Peter Hain, a senior Labor politician, told the BBC.

Advisers to Brown and Clegg were eager to quash reports that the two men had a testy telephone exchange Friday night. But they are said to have a prickly relationship.

Although their left-leaning parties are, in many ways, more natural allies than the Liberal Democrats and the Conservatives, a “Lib-Lab” pact could be difficult if Brown insisted on remaining as prime minister. The dour Scotsman has some of the lowest approval ratings of any leader in British history.

On the other side, Clegg is in serious negotiation with a party whose leader he accused of showing “breathtaking arrogance” during the election campaign.

In what looked like a somewhat awkward moment, the three men appeared together Saturday for a ceremony commemorating the Allied victory in Europe in World War II and the soldiers who died to secure it.

None of the three party leaders looked particularly pleased to be there, though their somber faces may merely have been byproducts of the solemnity of the occasion.