The Greens and Labor will attempt to move a motion of no confidence in the home affairs minister, Peter Dutton, after the tabling of a Senate report finding he misled the parliament in relation to the au pair controversy.

The motion will be brought on in the House of Representatives on Thursday after the Labor-dominated Senate committee concluded Dutton “had a clear personal connection and existing relationship with the intended employer of the au pair in the Brisbane case”.

Dutton was asked in parliament in March, when reports of the use of his ministerial discretion to grant tourist visas first surfaced, whether he could rule out “any personal connection or any other relationship between you and the intended employer of either of the au pairs”.

Dutton responded: “The answer is yes.” He said he had received no personal benefit from the decision and “I don’t know these people”.

The majority report from the Senate committee said: “Given his definitive answer in the House of Representatives, it is the view of the committee the minister misled parliament in relation to this matter.”

Dutton has faced political pressure over the use of ministerial powers in 2015, when he approved visitor visas to an Italian and a French au pair facing deportation.

The Italian woman planned to work for the family of Dutton’s former Queensland police force colleague Russell Keag. Dutton intervened in the case of the French au pair after the AFL’s chief executive, Gillon McLachlan, raised the young woman’s case on behalf of his South Australian relatives.

The Senate committee contended Dutton may not have intervened in the Adelaide case “if it was not for the fact it was raised through personal connections”. It said Dutton appeared “to have failed to give consideration to the damage to public confidence in the integrity of the immigration system that his actions could cause and, at best, reflects very poor judgment on the part of the minister”.

The majority report said Dutton’s use of his discretion does “not reflect community expectations of how such powers should be used”.

It also put a question mark over the material that was supplied to the committee over the course of its inquiries. “It is the view of the committee that substantial inconsistencies in evidence provided by the department during the course of the inquiry leaves significant doubt as to whether all relevant ministerial interventions have been captured by the inquiry.”

In advance of the report being tabled on Wednesday evening, Dutton – who has denied misleading the parliament – moved to discredit its conclusions. He branded the inquiry “a witch hunt”.

Dutton told reporters a Labor-Greens majority Senate report could only deliver a finding that he was “a bad person”.

“It will be a political report with political recommendations from the Labor party and the Greens, who have the numbers on that committee,” the home affairs minister said.

His objections were echoed by Coalition senators in a dissenting report that recommended Dutton be “commended for his prudent and diligent work as a minister” and he “ignore the majority report’s findings”.

Dutton has also been backed consistently by the prime minister, Scott Morrison.

The Greens will attempt to move the no confidence motion with Labor’s backing. The Tasmanian independent Andrew Wilkie is on board for the vote.

It is not yet clear whether the independents Cathy McGowan and Rebekha Sharkie will support the motion. Both told Guardian Australia on Wednesday night they wanted to read the Senate report before making a decision.

The majority Senate report made three recommendations, including that the government strengthen the minister’s tabling statements to parliament on ministerial interventions, by requiring the minister’s statements to declare whether or not each ministerial intervention was made in accordance with the ministerial guidelines.

It said the Senate should consider censuring Dutton “for failing to observe fairness in making official decisions as required by the statement of ministerial standards”, and Dutton should provide, “within three sitting days, an explanation to the Senate responding to the matters raised in this report”.