In an interview with CBC Radio's The House, Trudeau said Parliament is "getting bogged down with scandal and conflict."
"It's really frustrating to see the level of mistrust and disgust that Canadians are having towards Parliament, towards the prime minister right now. It's time the prime minister showed some leadership and actually came clean on everything he knew, and the only way we're going to be able to do that, unfortunately, is if everybody testifies under oath."
Trudeau earlier this week said Harper should testify under oath. Harper has not responded.
The Liberal Leader offered no specifics about what kind of probe he's advocating. "The RCMP's already investigating what's gone on in the Wright-Duffy affairs. They're trying to get to the bottom of this issue. There are lots of different ways of getting to testimony under oath. There are inquiries, there are various ways of doing it," Trudeau said.
Trudeau's challenge to Harper followed new claims by Senator Patrick Brazeau that he'd been offered "a back-room deal."
Brazeau said Claude Carignan, the government leader in the Senate, approached him Friday morning.
"And the back-room deal was that if I stood in [the Senate], apologized to Canadians and took responsibility for my actions, that my punishment would be lesser than what is being proposed,” Brazeau said.
Carignan told reporters his remarks had been misinterpreted by Brazeau.
Asked what he thought of Brazeau's accusation and Carignan's denial, Trudeau said, "I don't want to get into the 'he said, she said.'"
What is apparent is the Conservatives are doing anything they can to try to minimize the damage that has been caused by this entire affair to their reputation, to their credibility, to their capacity to actually address the many challenges Canadians are facing," he added.
The Senate is expected to vote next week on a Conservative motion to suspend Brazeau and fellow Senators Mike Duffy and Pamela Wallin without pay or benefits — a proposal the Liberals have said they won't support without amendments.
"We're pushing for openness and transparency and an opportunity to hear from these three Senators at committee. We have Mr. Harper deciding that he's going to dump all the responsibility on the three of them and try to create a serious penalty here that, to my mind, needs to be at least reasonably discussed before we enact something that's going to create precedents," said Trudeau.
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