David Cameron's Conservatives won the most seats in Thursday's parliamentary election but fell short of a majority and are seeking the support of Nick Clegg's third-placed Liberal Democrats, or Lib Dems, to end 13 years of Labour Party rule.
Britain's Conservatives entered detailed talks with the smaller Liberal Democrats on Sunday to look for ways to form a government, under pressure to make progress before nervous financial markets reopen on Monday.
Prime Minister Gordon Brown, whose Labour came a distant second, remains in office in a caretaker role. He stands ready to try for an alliance with the Liberal Democrats if they are unable to agree with the Conservatives.
The election was the first since 1974 to give no party overall control. It has come at a time when Britain's budget deficit is running at a peacetime record of more than 11 percent of national output, unnerving financial markets.
They want to see a stable government emerge as quickly as possible and start aggressively cutting the deficit.
"We are very conscious of the need to provide the country with a new, stable and legitimate government as soon as possible," said senior Conservative William Hague, one of the small team negotiating with the Lib Dems, as talks resumed.
"The initial meeting we had on Friday night and the meeting between the party leaders last night were both very constructive, very positive, very respectful of each other's positions in the nature of those meetings.
"So we are going into these negotiations very much in that spirit today," Hague told reporters.
The Lib Dems said the first rounds of talks had been mostly about process and Sunday's meeting would be the longest negotiation on substantive issues so far. Neither Cameron nor Clegg were attending the talks on Sunday.
The greatest stumbling block may well be electoral reform, a long-cherished ambition of the Lib Dems who would win far more seats if Britain switched from its winner-takes-all system to proportional representation.
Opinion polls in Sunday's newspapers suggested most Britons favoured a more proportional system of voting, but the Conservatives are firmly opposed to such a change.
The parties must overcome other key differences on economic policy, defence, immigration and Britain's stance towards Europe, but they could find common ground on issues such as lower taxes for the poor, education and the environment.
"The mood is good, there is a willingness to try and sort things out in the national interest," Conservative education spokesman Michael Gove, one of Cameron's closest allies, told BBC television.
He said it was important the two sides showed progress by Monday when the markets open, but that any agreement would allow them to feel comfortable and that it would last.
When asked if he would be prepared to give up his chance of a ministerial post to make room for a Lib Dem and help clinch a deal, Gove replied "yes" without hesitation.
He suggested several scenarios were possible, including a minority Conservative government supported in parliament by the Lib Dems on certain key issues, a more formal coalition with ministers from both parties, or something in between.
Senior Liberal Democrat Simon Hughes sounded a note of caution, warning that positions on electoral reform were very far apart and his party was suspicious of the Conservatives.
"We are wanting to get on with this as quickly as we can, but nobody thinks we can get a deal by tomorrow ... If it takes a few days, so be it," he told the BBC.
"They have sounded superficially accommodating (on voting reform) but fundamentally pretty unreconstructed, and the further you go away from the leadership the more unreconstructed they are," Hughes said.
"So our party is very suspicious of the Tory (Conservative) party being able to deliver."