Jane Philpott, who also served as Treasury Board president, said she no longer had confidence in Trudeau's government over the allegations that senior officials attempted to head off the prosecution of engineering giant SNC-Lavalin.
"I have been considering the events that have shaken the federal government in recent weeks and after serious reflection, I have concluded that I must resign as a member of Cabinet," Philpott said on Twitter.
"The solemn principles at stake are the independence and integrity of our justice system... Sadly, I have lost confidence in how the government has dealt with this matter and in how it has responded to the issues raised."
Philpott is said to be close to ex-justice minister and attorney general Jody Wilson-Raybould, who triggered the crisis for Trudeau's Liberal government.
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Last month, Wilson-Raybould testified before the House of Commons Justice Committee that Trudeau and his inner circle applied 'inappropriate' pressure on her, including 'veiled threats,' to intervene in the prosecution of SNC-Lavalin.
She said that from September to December 2018, officials 'hounded' her to ask prosecutors to settle the case out of court.
Last week, the opposition called for Trudeau's resignation and for launching a federal investigation to look into Wilson-Raybould's claims.
SNC-Lavalin was charged in 2015 with corruption for allegedly bribing officials in Libya between 2001 and 2011 to secure government contracts during former strongman Moamer Kadhafi's reign.
Wilson-Raybould refused, and the trial is set to proceed. Canada's first indigenous attorney general, she was shuffled to veterans affairs in January, and a month later resigned from cabinet.
Days later, Trudeau's longtime friend and top adviser Gerry Butts also quit.
Trudeau said he 'completely disagrees' with his former attorney general's characterisation of events, insisting that he and his team were rightly looking to safeguard up to 9,000 Canadian jobs, including in his own Quebec electoral district.
Wilson-Raybould referred to those moves as improper "partisan political considerations."
Trudeau has insisted that he made clear to his former attorney general that the "decision around SNC-Lavalin was Wilson-Raybould's and hers alone to make."
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