Immigration Minister Marc Miller says Prime Minister Justin Trudeau should remain at the helm of the Liberal party after a devastating loss in a key Toronto riding but he said a period of introspection will be important to go through.

Mr. Miller, who spoke in Montreal on Wednesday morning, was asked by reporters about Mr. Trudeau’s future after Liberal Leslie Church, a former chief of staff to Deputy Prime Minister Chrystia Freeland, lost to Conservative candidate Don Stewart in the long-held Liberal riding of Toronto-St. Paul’s. The riding was previously held by former cabinet minister Carolyn Bennett, who is now the ambassador to Denmark.

Mr. Trudeau, who has faced months of questions about his leadership with slumping polls and widespread voter dissatisfaction, is now under even more pressure after the by-election results. The Conservative win opens the prospect that the party has an even wider path to victory in the next federal election. For the Liberals, the result reflects how precarious the party’s future has become.

Trudeau to remain party leader as Liberals demand urgent changes after stunning by-election loss

Mr. Miller said Wednesday that the result in Toronto-St. Paul’s is a loss that should not be minimized.

“I think a lot of us have to take a step back and give our heads a shake, screw it on a little better,” he said. “Stop the navel gazing and get back on the horse and fight for Canadians. “

The minister, who is a close friend to the Prime Minister, said his advice to Mr. Trudeau as a minister and a colleague is “absolutely stay on.”

Mr. Miller said Canadians want to see the government fighting challenges such as affordability. He said there is “obviously a period of introspection” that occurs after any win or loss.

“The quicker that we can get back on the horse and keep fighting for Canadians, I think the better,” he said.

He said the Prime Minister is the person best placed to take on Conservative Leader Pierre Poilievre, who has a very different view for what the country looks like and the direction that it is going in.

“I love my country,” Mr. Miller said. “I’m going to fight for every inch of it. I believe the Prime Minister is going to do it as well.”

Elections Canada defends vote counting despite Toronto-St. Paul’s by-election delay

The Globe and Mail has spoken with 10 Liberals, including MPs, staffers and senior operatives. They described a party in shock, with no road map for how to change its position with the electorate. They also questioned how the party so badly misread the mood in one of its safest seats, wondered if headquarters still knows how to run an effective campaign, and worried about a disconnected Prime Minister’s Office.

The Globe is not identifying the sources who were not permitted to publicly discuss internal party dynamics.

Longtime Liberal MP John McKay, who is not seeking re-election, would not comment on Mr. Trudeau’s leadership when speaking to The Globe. He campaigned for Ms. Church in Toronto-St. Paul’s last Saturday and said that, in his view, the by-election amounted to a “referendum” on Israel as much as anything else and it seems to be what “put the Conservatives over the edge.”

Nik Nanos, chief data scientist of Nanos Research, said Mr. Trudeau’s brand is an “integral part” of the Liberal party and for that reason “it’s hard to see knives coming out for him.”

“However, he has to decide what’s in the best interest of the party and what he thinks is in the best interest of the country,” Mr. Nanos said.

“What’s clear, at least from the by-election in Toronto-St. Paul’s, is that the country is in a mood for change. We know that in the polling numbers nationally and it’s been shown in the by-election in St. Paul’s.”

Opinion: Regardless of leader, the Liberals are at risk of a worse fate after Toronto-St. Paul’s by-election

Mr. Nanos noted the Liberals put a lot of capital in to trying to win the riding and “it wasn’t enough to hold on.”

Shachi Kurl, president of Angus Reid Institute, said her institute released data on Monday that shows that among voters who might still consider voting Liberal, there are individuals who do not see Mr. Trudeau as the issue but rather the government’s lack of progress on issues they care about.

She said Mr. Trudeau, who is known to like boxing, is sporting a “stunning shiner” after the by-election loss. But she said “changing the fighter in the middle of the match” may not make a difference.