Mr. Johnson, who has been eager to go to the voters since he became prime minister in July, is expected ask Parliament later Monday to schedule an election for Dec. 12. But under a 2011 law, he would need the support of two-thirds of the House of Commons to do so.
The Labour Party, which is deeply divided on the merits of holding an election now, is likely to reject Mr. Johnson’s motion. Analysts said that the situation was fluid and that Labour could shift, particularly since the party’s leader, Jeremy Corbyn, is viewed as more open to a campaign than some of his rank-and-file members.
Over the weekend, a new strategy emerged that could give Mr. Johnson another route to a vote. The Liberal Democrats and the Scottish National Party said they would back a one-line amendment to the 2011 law, known as the Fixed-term Parliaments Act, that would allow an election on Dec. 9, now that the European Union has offered an extension until Jan. 31.
Each party has its own reasons for wanting a quick vote. The Liberal Democrats are eager for an election before Britain leaves the European Union because they are running on a platform of revoking Brexit altogether. That message that would be rendered irrelevant in any election held after Britain had already left.
The Scottish National Party would like an election as soon as possible because its former leader, Alex Salmond, faces trial next year on charges of attempted rape and sexual assault — an unpalatable backdrop for its campaign.
Mr. Johnson and his allies are likely to hammer away on the need for an election if Labour resists, blaming Labour for the prime minister’s inability to keep his promise to leave the European Union on Oct. 31, “do or die.”
The Conservatives view a campaign as a way to paint Mr. Corbyn as afraid of facing the voters, and believe that they have the momentum.
Matina Stevis-Gridneff reported from Brussels, and Mark Landler from London.