Greens senator Lidia Thorpe’s undisclosed relationship with a former bikie boss will head to a parliamentary probe as she denies any wrongdoing.

Senator Thorpe dated former Rebels outlaw motorcycle gang president Dean Martin while sitting on a parliamentary law enforcement committee.

The Victorian senator acknowledged she should have disclosed the relationship but denied any wrongdoing while on the committee.

The Senate voted on Tuesday to refer the matter to the privileges committee, which investigates whether parliamentarians have complied with disclosure requirements.

The committee will investigate whether her failure to declare the relationship obstructed or improperly interfered with the committee’s work or constitutes contempt.

Senate President Sue Lines said it was important senators not interfere with the free exercise of committees or sit on the committee if there is a conflict of interest.

She said the revelation had met the threshold for it to be investigated by the privileges committee after she received a letter from Senator Thorpe on Monday saying she would support the referral.

A defiant Senator Thorpe told the Senate she was “not going anywhere”, but acknowledged she had made a mistake.

“I strongly reject any suggestion I would do anything other than comply with the committee’s requirements and I note no one has offered any evidence to the contrary,” she told the Senate.

“However, I accept that I should have disclosed this.”

Senator Thorpe resigned from the party’s leadership team in the wake of the revelations.

Labor senator Anthony Chisholm said her actions could potentially carry serious consequences given the sensitive law enforcement bodies the committee she sat on oversees.

Senator Chisholm said an investigation was necessary to ensure Australians could trust its parliamentarians act with integrity.

Senior Liberal senator Simon Birmingham said it was important parliamentarians be seen to be free of any improper influences

“The allegations are serious ones,” he said.

Both the government and opposition also called on Greens Leader Adam Bandt to explain why he was kept in the dark when members of his staff knew of the relationship.

Mr Bandt told parliament his chief of staff should have informed him when he became aware.

“I should have been told, but I wasn’t,” he said.

Mr Bandt said he had since “counselled” his chief of staff and other senior staff in his office about directly raising matters with him.

He said Senator Thorpe had also assured him no confidential information from the committee had been shared with Mr Martin.

The Greens’ internal complaints processes are also being reviewed.

-AAP