Prime Minister Justin Trudeau of Canada faced the stiffest challenge to his leadership from fellow elected Liberal Party members on Wednesday during a closed-door meeting where he was urged to resign to avoid torpedoing the party’s chances in the next election.

For more than a year, the Liberals under Mr. Trudeau have trailed the Conservative Party by double digits in polls, suggesting that the Liberal Party could face a crushing defeat in the next election, which must be held by next October.

Panic within the party intensified after the Liberals recently lost two special parliamentary elections in districts that had been considered their strongholds.

The growing dissatisfaction played out on Wednesday, when most of the 153 Liberal members of Parliament gathered in Ottawa for a scheduled caucus meeting.

While caucus proceedings are typically secret, Mr. Trudeau, according to Canadian news media citing unnamed sources, was presented with a letter signed by about two dozen caucus members calling on him to step down.

The letter has been circulating for several days, but has been a closely held secret.

About 20 Liberal members criticized Mr. Trudeau’s leadership after the letter was read aloud during the three-hour-and-17-minute meeting, according to Canadian news outlets.