Prime Minister Gordon Brown, whose Labour Party sustained damaging losses, signaled that he would not immediately step down, even though his party had lost its majority, shedding at least 91 seats in the House of Commons while the opposition Conservatives surged ahead with a 97-seat gain. But, Mr. Brown said, he would welcome discussions with other party leaders, including Mr. Clegg, if the Liberal Democrats failed to strike a deal with the Conservatives.

“It is my duty as prime minister to take all steps to ensure Britain has a strong, stable and principled government,” Mr. Brown said Friday, adding that he had asked senior civil servants to assist all the parties in talks to devise an exit from the impasse, the first of its kind since 1974.

Although the Liberal Democrats failed to make the gains forecast before the vote on Thursday, they still seem set to play a pivotal role in the interparty negotiations to form a new government. The political minuet between the party leaders — common in parts of continental Europe where coalitions are the norm, but rare in Britain’s political culture — began when Mr. Clegg said he believed Mr. Cameron should have the first right to form a government.

Then Mr. Brown appeared outside 10 Downing Street — the prime ministerial residence and seat of power — to offer an alliance with Mr. Clegg based on a shared approach to the country’s economic crisis and to reforms in the voting system, a central demand of the Liberal Democrats.

Mr. Brown stressed that he was speaking as prime minister, underscoring his continued claim to office, despite his poor showing in the polls.

Finally, Mr. Cameron delivered a statement that offered some concessions — but not guarantees — to the Liberal Democrats on economic measures and electoral reform, while making clear that Conservatives disagreed with their potential allies on other matters such as immigration, the relationship with Europe and defense.