“I experienced a consistent and sustained effort by many people within the government to seek to politically interfere in the exercise of prosecutorial discretion,” Ms. Wilson-Raybould said.

The former justice minister recounted how senior government officials, mostly from Mr. Trudeau’s office, attempted to persuade her to order prosecutors to cut a plea deal with SNC-Lavalin, which is based in the politically important province of Quebec. A plea deal would have allowed SNC-Lavalin to avoid a decadelong ban on bidding on government contracts in Canada and elsewhere. These make up a significant portion of the company’s revenue.

“There were expressed statements regarding the necessity of interference in the SNC-Lavalin matter, and the potential for consequences and veiled threats if an [out-of-court settlement] was not made available to SNC-Lavalin,” she said.

Ms. Wilson-Raybould said Mr. Trudeau encouraged her in a Sept. 17 meeting to “find a solution here for SNC-Lavalin, saying that if there was no [plea deal] there would be many jobs lost and SNC-Lavalin would move [its headquarters] from Montreal.” She said she told Mr. Trudeau that she had done her due diligence on SNC-Lavalin and she wasn’t going to interfere in a decision by prosecutors to not pursue a plea deal with the company.

Mr. Trudeau and other senior officials have denied any wrongdoing in their interactions with the former justice minister. At a Wednesday night press conference in Montreal, the Canadian leader said he “completely disagree[s] with the former attorney general’s characterization of events” and defended the work of his top aides.

He added that there were discussions about potential job losses in the event SNC-Lavalin was convicted. But, he said, the final decision on the company’s prosecution “was Ms. Wilson-Raybould’s and hers alone.”

Canada’s ethics watchdog launched a probe into the SNC-Lavalin matter after the Globe and Mail newspaper reported the allegations. In response to a lawmaker’s question, Ms. Wilson-Raybould said that she didn’t believe the lobbying effort violated any laws. But throughout the three-hour-plus hearing, she described the effort as inappropriate.

Canadian prosecutors filed bribery and fraud charges against SNC-Lavalin in 2015, related to activity in Libya during 10 years ended in 2011. The company has also faced bribery charges at home. Its former chief executive pleaded guilty this month to charges related to a bribery scandal involving the construction of a Montreal hospital.

SNC-Lavalin Chief Executive Neil Bruce said last week that an out-of-court settlement would be in the public interest because it would ensure employees, pensioners and suppliers wouldn’t be harmed. The company operates in over 50 countries and employs 50,000 workers world-wide.

In January, Ms. Wilson-Raybould was told she was being moved from the high-profile justice portfolio to the veterans ministry. She told committee members she believes the move was triggered by her refusal to direct prosecutors to drop the criminal prosecution of SNC-Lavalin.

She stepped down from the cabinet this month, days after the allegations of judicial interference emerged. In her testimony, she said she resigned because “I did not have confidence to sit around the cabinet table.”

Ms. Wilson-Raybould’s testimony represents a pivotal moment for Mr. Trudeau, whose reputation has taken a beating from the SNC-Lavalin affair. His political brand of a modern, transparent leader who was willing to give his cabinet greater leeway in crafting policy helped lift him to power in the fall of 2015.

“This story is potentially toxic for the prime minister’s image,” said Daniel Beland, a political analyst and director of McGill University’s Institute for the Study of Canada in Montreal. Exacerbating matters, Mr. Beland said, was the inability of Mr. Trudeau and his aides to handle the crisis with consistent descriptions of what unfolded.

Ms. Wilson-Raybould said she was told in mid-December by a top adviser to Mr. Trudeau, Michael Wernick, that the prime minister was “going to find a way to get it done one way or the other, so he is in that kind of mood and I wanted you to be aware of it.”

Last week, Mr. Wernick delivered testimony in which he said that at no time did Ms. Wilson-Raybould face inappropriate pressure to strike an out-of-court deal with SNC-Lavalin. He acknowledged, though, that he spoke to Ms. Wilson-Raybould about the implications of prosecuting SNC-Lavalin. “I conveyed to her that a lot of her colleagues and the prime minister were quite anxious about what they were hearing and reading in the business press about the future of the company,” he said.

Polling since the uproar emerged in early February indicates Mr. Trudeau and the Liberal government are bleeding support, less than eight months before the next national election. Surveys from Ipsos Public Affairs and the Angus Reid Institute indicate the opposition Conservatives hold a lead over the governing Liberals in terms of the popular vote.

The fate of SNC-Lavalin is an important issue in Quebec, Canada’s second-largest province and a pivotal electoral battleground. The province’s large pension fund, Caisse de depot et placement du Quebec, is SNC-Lavalin’s biggest shareholder, with a 20% stake. The company employs 9,000 across Canada, including 3,400 in Quebec.

Write to Paul Vieira at paul.vieira@wsj.com and Kim Mackrael at kim.mackrael@wsj.com