Labor used Question Time to raise allegations that Ms Howlett had engaged in an affair with the chief executive of the Tasmania JackJumpers, prompting perceived conflict of interest issues in her role as Sport Minister.

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Mr Gutwein met with Ms Howlett and another individual - described as a "support person" - the day before she resigned from cabinet last week.

He claimed he was unaware of any other allegations before they were brought to him by the media.

In the announcement, Mr Gutwein said her resignation was due to the death of her brother two weeks earlier, but Labor disputed this and demanded to know the identity of the other person in the meeting.

Deputy Labor leader Anita Dow said there were "persistent allegations" of an affair leading up to the resignation, and asked whether Mr Gutwein was intentionally avoiding answering questions on the matter.

"When Adam Brooks was facing allegations of defrauding women, you said you'd asked him about the allegations. He had denied them, and you had taken his answers on face value," she said.

"If we're to believe your version of events, this is exactly what you have done in relation to the allegations faced by Jane Howlett.

"Is it your deliberate strategy to play dumb when you want to cover up allegations of unacceptable conduct by members of your government?"

Labor's concerns centred on the allocation of government funds to the JackJumpers while an alleged affair was occurring.

Mr Gutwein said Ms Howlett had told him "there was no truth to the rumours and that there was no conflict of interest", and he believed her.

He said Ms Dow could make the allegations away from parliamentary privilege if she was so sure of them.

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"If the deputy leader of the opposition wants to stand behind these sorts of grubby allegations, which she's very clearly lining up Jane Howlett for, then get outside and make them outside," Mr Gutwein said.

"Have the courage of your own convictions if you believe in what you're actually putting forward."

He then took aim at Labor leader Rebecca White over the party's handling of sexual misconduct allegations levelled at Franklin MHR David O'Byrne last year.

Mr O'Byrne is no longer a member of Labor caucus, but remains the Labor member for Franklin.

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Labor MHRs had attended the first day of Parliament wearing red face masks, but Mr O'Byrne was conspicuous in his white face mask.

Mr Gutwein said it was a reminder of the party's internal turmoil of last year.

"I would make this point: have a look at the lot of you," he said.

Jane Howlett is the second minister to resign in as many weeks after Sarah Courtney took her leave from cabinet.

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