"I have no hesitation in asking Ministerial Services to look into that. Regardless, the minister has already paid the ultimate price. If there is anything that has financial implications then I would have no hesitation asking for that to be dealt with as well," she said.
"I will ask them to do that."
Ministerial portfolios
Lees-Galloway, 41, has been the MP for Palmerston North since 2008. He has held the ACC, immigration, and workplace relations and safety portfolios since 2017.
Those portfolios will now be taken up by Carmel Sepuloni, Kris Faafoi and Andrew Little respectively until the election. Lees-Galloway will also stand down at the election.
Lees-Galloway, married with three children, was sacked after a third party contacted Ardern's office with claims of the inappropriate relationship. That followed an earlier contact with the office of National Party leader Judith Collins.
Ardern avoided providing detail so as not to identify the woman involved, but said she was advised that the consensual relationship had ended several months ago. While the woman had worked in Less-Galloway's office, the relationship had started while she was working in one of his agencies.
Nevertheless, Ardern said she no longer had confidence in Lees-Galloway's judgement.
"I am wary about making moral judgements here," she said.
"For me this is about a demonstration of judgement; it's about whether I maintain confidence.
"Over a sustained period of time - a long period of time – our Minister of Workplace Relations has not modelled behaviour that is in keeping with his office."
Ardern said she had not been aware of the relationship, and noted that many rumours circulate around Parliament, especially during the more heated environment in the lead up to an election.
She did not respond specifically when asked whether she would issuing any new direction to her caucus and other ministerial staff, given the number of people who would have been aware of the relationship in question.
"These issues are constantly a reminder to everyone of the need to maintain a set of operating principles, a set of behaviours that are in keeping with what our communities expect of us."
Unbecoming behaviour
The sacking comes in a bad week for the image of the country's parliamentarians.
On Monday, National's Rangitata MP Andrew Falloon was forced to resign effective at the coming election following revelations he had sent unsolicited sexually explicit material to young women online.
That claim had been sent late last week to Ardern's office, which had then passed it onto Collins' office to deal with. The following day he resigned with immediate effect after Collins said Falloon's earlier accounts had been untrue.
Today, Ardern said she hoped the sackings would not tarnish Parliament's reputation to the extent that it reduced turnout for the September 19 vote.
In a statement, Lees-Galloway said he accepted the Prime Minister's decision and apologised "absolutely". He had also apologised to his family for letting them down.
"I also apologise to anyone who has been hurt by my actions."
