London, England (CNN) -- The United Kingdom appeared Monday to be inching towards having a new government, as two parties scheduled meetings behind closed doors after last week's inconclusive elections.
The Conservatives -- who won the most seats, but fell short of a majority -- are meeting Monday night, a party spokesman confirmed.
The Liberal Democrats, who came third but hold enough seats to put the Conservatives in power, have two meetings scheduled for Monday, a party spokesman told CNN.
Party leader Nick Clegg said Monday "a prolonged period of uncertainty" about who would govern Britain is "not a good thing."
"We have been working around the clock, meetings, telephone calls constantly going on, to provide that clarity as soon as possible," he said.
It's extremely rare for no one party to win a majority in the British House of Commons. The last time the country had a so-called "hung parliament" was in 1974, and voters were back at the polls within a year of that happening.
It's not clear if the Conservatives and Liberal Democrats are discussing a formal coalition or Liberal Democrat support for a minority Conservative government.
Liberal Democrat lawmakers are meeting around lunchtime, and the party's federal executive is meeting in the evening, spokesman Phil Reilly said.
Party rules say both groups must approve any deal that would affect the party's political independence by a 75 percent majority.
Both sides said publicly Monday that talks were going well, but Reilly said not to read too much into the party meetings taking place, saying they were an "update on how things are going."
There are wide gulfs between the Conservatives and Liberal Democrats in key policy areas, including the electoral system, immigration, the economy and London's relationship with Europe.
Clegg said his party would continue to be guided by its ambitions of bringing "stability back to the British economy" by introducing "big changes" in tax reform, the way the school system works, and the way the economy is run as well as "the way the political system is organized."
Party officials talked through the weekend.
"We've had good discussions. We intend to meet again over the next 24 hours," William Hague, a top adviser to Conservative leader David Cameron, told reporters after the talks broke Sunday evening.
"We agree the central part of any agreement will be economic stability and a reduction of the budget deficit."
Spokesmen for Labour Prime Minister Gordon Brown and the Liberal Democrats declined to comment for CNN on rumors that Clegg and Brown were also meeting on Monday.
Clegg met with Conservative leader David Cameron on Saturday, both sides said, and had an "amicable discussion" with Brown on Sunday during a meeting at the Foreign Office, the Labour Party's press office said.
Clegg addressed a Saturday protest by hundreds of protesters in London who were demonstrating in favor of proportional representation, a system supported by the Liberal Democrats.
"I never thought I'd see Londoners protesting for proportional representation," Clegg said.
"Take it from me, reforming politics is one of the reasons I went into politics. I campaigned for a better, more open, more transparent new politics every single day of this general election campaign."
The Lib Dems say the current electoral system is unfair and leaves them under-represented in Parliament.
They say the number of seats they have in the House of Commons fails to reflect the number of votes they won across the country, and they believe each party's allocation of seats should reflect the percentage of the national vote they get.
For example, the Conservatives got 36 percent of the vote, but a total of 306 of the 650 seats in Parliament.
Under proportional representation, they would have 234 seats.
Labour got 29 percent of the vote and a total of 258 seats, but the Liberal Democrats' 23 percent of the popular vote amounted to 57 seats -- little more than a third of the roughly 150 they would have won with proportional representation.
It's unclear how far Cameron will go on electoral reform. But he said in an e-mail to party members that he is willing to compromise on some issues.
"There are also areas where I believe we in the Conservative Party can give ground," he wrote, "both in the national interest and in the interests of forging an open and trusting partnership. For example, we want to work with the Liberal Democrats to see how we can afford to reduce taxes on the lowest paid."
Parties smaller than the Liberal Democrats hold too few seats in Parliament for them to be realistic choices for the Conservatives, analysts have said.
The last time Britain had a hung parliament was in February 1974, when Edward Heath's Conservatives gained more votes but fewer seats in Parliament than Labour.
The Conservatives proved unable to form a deal with the Liberal Party, and voters found themselves back at the polls by October.