A day after the bombshell resignation of Prime Minister Justin Trudeau's closest adviser, the SNC-Lavalin controversy shows no sign of fading as opposition parties in the House of Commons unite to demand a public inquiry.

Conservative Leader Andrew Scheer said Tuesday the gravity of the core allegation — that there was undue political influence on the criminal prosecution process — demands a thorough study by an independent arbiter.

Watch the Power Panel discuss Wilson-Raybould's appearance at a cabinet meeting on Power & Politics

Francoise, Stockwell, Jen and Tim discuss JWR's appearance at cabinet and the next steps of the justice committee. 10:14

"We cannot claim to be a country under the rule of law when political agendas can dictate the course of justice," Scheer said. "And that's precisely what the prime minister and his office stand accused of."

The party's deputy leader, Lisa Raitt, said a public inquiry is the best way "to get to the bottom of something so crucial to the rule of law."

Amid the calls for an inquiry, the House of Commons justice committee will reconvene today to continue its study of a recent news report that senior members of the Prime Minister's Office pressured then-justice minister Jody Wilson-Raybould to help Quebec-based multinational engineering firm SNC-Lavalin avoid prosecution on bribery and fraud charges in relation to contracts in Libya.

Gerald Butts, Trudeau's principal secretary and right-hand man, resigned his position Monday, stating that neither he or anyone else in the PMO pressured Wilson-Raybould to direct the Public Prosecution Service of Canada to draft a deferred prosecution agreement (DPA) — a legal tool resembling a plea deal — for SNC-Lavalin.

"At all times, I and those around me acted with integrity and a singular focus on the best interests of all Canadians," Butts said Monday.

Trudeau also has insisted there was no wrongdoing — that he told Wilson-Raybould last fall that any decisions on matters involving the director of public prosecutions were hers alone to make.

In a surprise move, Wilson-Raybould met with Trudeau and his cabinet Tuesday. Speaking to reporters before question period, Trudeau said she asked if she could address her former cabinet colleagues a week after her departure.

Wilson-Raybould spoke briefly with reporters after leaving that cabinet meeting. When asked if she was pressured over SNC-Lavalin, as the media report suggested, she said only that she is still "working with" her lawyer.

Former attorney general Jody Wilson-Raybould says she's still working with her lawyer to see what she can legally say, but that she remains a member of the Liberal caucus. 0:43

"As a member of Parliament, my ethical and professional responsibilities as a lawyer are layered and incredibly complicated," she said. She also confirmed that she is still a Liberal MP.

The Liberal government maintains that the federal ethics commissioner's ongoing examination of the still-unsubstantiated allegations is an independent probe therefore a public inquiry is an unnecessary measure. Conservatives say the ethics commissioner is essentially toothless.

Speaking in the Commons, Liberal MP Marc Miller, a parliamentary secretary and personal friend of the prime minister, said demands for an independent inquiry were "absolutely premature."

"Despite the many media reports, what we have so far is unsubstantiated allegations. Indeed, we have two high-profile resignations, but we don't know the substance of the allegations," Miller said. "There's very, very little substantiated fact ... I will readily concede that we don't know enough. The issue is whether we are publicly entitled to enough."

Conservative Leader Andrew Scheer supports an NDP motion in the House of Commons today to launch a pubic inquiry into the Prime Minister's Office amid the SNC-Lavalin case, especially in the wake of the Prime Minister's principal secretary Gerry Butt's resignation from the PMO Monday. 1:08

Miller also said staging an inquiry at this time — while criminal matters related to SNC-Lavalin are still before the courts — would be ill-advised, since parliamentarians generally refrain from discussing matters under judicial review.

Scheer said Butts' departure "does not in any way settle this matter. In fact, it presents even more questions that must be answered."

"When the Justice Department said 'no' to SNC-Lavalin, the Prime Minister's Office wouldn't take 'no' for an answer," Scheer said. "Conservatives on the justice committee will continue to demand a thorough and public investigation, and all other options remain on the table. Canadians deserve answers and I will continue to do everything in my power to get them."

Gerald Butts has resigned from his position as senior political adviser to Prime Minister Justin Trudeau. (Sean Kilpatrick/Canadian Press)

NDP MP Charlie Angus, the party's ethics critic, tabled an opposition motion Tuesday that formally demands an inquiry into the political interference allegations.

Angus said Butts' departure — he calls the former staffer the "architect of the Sunny Ways" Trudeau playbook — could provoke a "political revolution."

"For Gerry Butts to resign shows how much damage [the scandal] has done inside the Prime Minister's Office ... If Mr. Butts is willing to take a jump for the prime minister, at this point, it shows that they're in free fall and total damage control," Angus said in an interview with CBC News Network's Power & Politics.

"The best thing the prime minister could do to restore public confidence is come into the House and agree to an independent inquiry ... or else these questions are going to continue."

Commons committee to probe interference allegations

The Liberal and opposition members of the justice committee are expected to squabble today over who should be called to testify at the committee, and just how wide-reaching the parliamentary probe should be.

At the top of the opposition witness wish list is Butts himself and Wilson-Raybould, who resigned from cabinet last week after the Globe and Mail published its initial report.

"It's potentially possible, but there's a lot of water to go under the bridge yet," says cabinet minister Ralph Goodale on Power & Politics. 8:18

Wilson-Raybould had been demoted from the high-profile justice portfolio to the Veterans Affairs ministry in January.

Wilson-Raybould has stayed silent on the allegations, claiming that solicitor-client privilege prevents her from speaking publicly; as attorney general, she was the government's top lawyer.

She has taken the highly unusual step of retaining Thomas Cromwell, a recently retired Supreme Court justice, as her legal counsel as the scandal enters a new phase.

While the Liberal-controlled justice committee has agreed to study the matter, Liberal MPs defeated an NDP motion last week that would have compelled Butts and Wilson-Raybould to appear.

Following normal parliamentary procedure with respect to committee planning, members will discuss which individuals they want to call before the committee and define the scope of its investigation in private. The opposition parties had demanded these proceedings be held in public, but Liberals successfully pushed for closed-door discussions.

The parliamentary probe itself is expected to be televised.

More to come?

Opposition members have pointed to one line of Butts' resignation statement in particular as indicating that there might be more developments to come.

"My reputation is my responsibility," Butts said, "and that is for me to defend. It is in the best interests of the office and its important work for me to step away."

Not satisfied with a committee study alone, NDP Leader Jagmeet Singh is also demanding that Trudeau waive solicitor-client privilege to allow Wilson-Raybould to speak freely at a public inquiry.

Trudeau has said the privilege question is complicated and he is awaiting advice from current Attorney General David Lametti on what he can say in public. He has also said some aspects of the government's handling of the case are protected by cabinet confidentiality.

Speaking to reporters in B.C. a week out from the Burnaby South byelection in which he is running, Singh said intransigence by Liberal members of the justice committee demands another forum for investigation.

"The scandal cuts to the heart of our democracy," Singh said. "Canadians deserve a government that works for them, not a powerful multinational corporation that has deep ties to the Liberal Party."

Trudeau thanks Butts for his service

​In a tweet Monday, Trudeau said Butts served Canada with "integrity, sage advice and devotion." He thanked the former staffer for his service and "continued friendship."

In addition to the political partnership, the prime minister is close friends with Butts — a relationship that dates back to their time as students at McGill University in Montreal, where they were members of the campus debating club.

Born in Glace Bay, N.S., a coal-mining town on Cape Breton Island, Butts worked on public policy in Ontario before becoming a senior staffer under former Liberal premier Dalton McGuinty at Queen's Park.

Butts then made the leap to federal politics and helped chart Trudeau's political future as leader of the Liberal Party and later prime minister.

Praised by his allies as a brilliant mind, and vilified by foes as the political puppet master behind the prime minister, Butts said Monday he is proud of his time as Trudeau's top adviser.