Labor senator Murray Watt says the Senate’s one-day inquiry of the Peter Dutton au pair controversy needs to be extended because there are too many unanswered questions about the affair.

Watt says he hasn’t had a chance to talk to his Senate colleagues about it, but new evidence from the past two days means the inquiry should be lengthened.

“This whole au pair affair is just getting messier by the day,” Watt told ABC radio on Friday.

“We’ve now got directly contradictory evidence between the minister [Peter Dutton], his department and the former head of border force [Roman Quaedvlieg], about what involvement Peter Dutton and his minister’s office had in this entire affair.

“I think it just shows the need for this Senate inquiry to keep looking into this and for Peter Dutton to actually start answering questions to parliament.”

On 23 August the Senate referred the allegations concerning the inappropriate exercise of ministerial powers, with respect to the visa status of au pairs, to the Legal and Constitutional Affairs References Committee for inquiry and report by 11 September.

But Watt says the single-day hearing was not enough.

Following Wednesday’s hearing, Quaedvlieg sent a letter to the inquiry calling into question Dutton’s evidence to parliament that he did not know the employers of the au pairs under scrutiny.

Quaedvlieg claimed he had fielded a phone call in 2015 from Peter Dutton’s office seeking help for a “mate” of the minister over an Italian au pair in detention at Brisbane airport.

Dutton hit back on Thursday, labelling Quaedvlieg’s claims “entirely false” and accusing him of fabricating evidence because he is “bitter about the loss of his job” as head of Border Force.

In a blistering statement, Dutton said both Quaedvlieg’s claims and a Fairfax Media article detailing them were misleading and defamatory.

Quaedvlieg’s letter states that in mid June 2015 he received a call from Dutton’s chief of staff, Craig Maclachlan, who said he was ringing on behalf of the home affairs minister, who he referred to as “the boss”.

But Dutton said it was “impossible for this conversation to have occurred” because Maclachlan was not employed by him until 7 October 2015 and Maclachlan could not have had knowledge of the matter because he was not employed by the department of immigration either.

“Moreover, I did not instruct any member of my staff to call Mr Quaedvlieg in relation to this matter. Nor did any member of my staff speak to Mr Quaedvlieg about it.”

Watt said on Friday that it was possible that Quaedvlieg had made up his latest allegations but that’s why the Senate inquiry ought to be extended.

“And we would really appreciate greater participation by both Mr Quaedvlieg and Mr Dutton in that inquiry,” he told ABC radio.

“We have found it impossible to get answers from Mr Dutton’s department to very basic questions about the chain of events that led to these au pairs being released, and any other matters.

“The issue for Peter Dutton is under Westminster conventions he is obliged to provide full and frank answers to parliament and he has not done that.

“The only information that he has provided to parliament to date was either misleading or very tricky. He has claimed to have had no personal connection to the people involved when we now know that in at least one case he does have a personal connection, in that it’s someone he worked with in the Queensland police force.

“The thing that really annoys people about this whole affair is the complete double standards that Peter Dutton and other ministers have engaged in.

“We had evidence at the Senate inquiry this week from migration agents who told us about the long, arduous process they have to go through in order to get visas for much more deserving cases [than] these people, but here we’ve got a couple of instances where, just because you know the right person, or play polo, or have an au pair, you can make a phone call on a Sunday afternoon to a minister and get something approved within an hour.”

Watt acknowledged that Quaedvlieg was sacked for misbehaviour in March and is the subject of a corruption investigation over allegations he helped a junior staff member, with whom he was in a relationship, get a job at Sydney airport.