LONDON — Prime Minister Boris Johnson, stymied by Parliament on his plan to leave the European Union by the end of the month, challenged lawmakers on Thursday to approve a general election in December, hoping to win a popular mandate to carry out his vision of a swift Brexit.

But the opposition Labour Party reacted coolly to Mr. Johnson’s proposal, which he will bring before Parliament on Monday, viewing it as an act of political gamesmanship rather than a serious effort to find a path out of the morass that has enveloped Britain since it voted in 2016 to leave the European Union.

Throwing the question of Brexit back to the voters has been seen as a way to break out of a cycle of political paralysis. But the maneuvering in the wake of Mr. Johnson’s announcement showed that even this bid could fall prey to the same political forces that have subverted all previous efforts.

Mr. Johnson, who has already been forced to break his word by requesting an extension of the Brexit deadline until Jan. 31, presented the opposition with a quid pro quo: he would give members more time to deliberate over his deal with the European Union if they agreed to back an election on Dec. 12.