Ardern said today she immediately sought assurances from Mallard that he was taking appropriate steps to make Parliament safe.
He is seeking to do that job, she said.
Asked if Parliament was safe for women, Ardern replied:
"Well, it needs to be."
While those who shared information for the Francis report spoke under the condition of anonymity, Ardern said Parliament still had a duty to keep people safe.
Asked if there was a rapist in Parliament at the moment, Ardern said Mallard would provide more details.
Ardern said the choice of reporting to police was up to victims.
"We need to first ensure victims have the support they need," she said.
Ardern said yesterday's report showed there was still a huge amount of work to do.
Deputy Prime Minister Winston Peters has called Mallard's comments "repugnant" and said the alleged offender is not a parliamentary staffer or someone who works for a political party - though he wouldn't say what he was basing that on.
Yesterday, Mallard and independent reviewer Debbie Francis released a review of bullying and harassment at Parliament, which revealed 14 people who said they had been the victim of a sexual assault in the parliamentary workplace.
All the allegations related to male-on-female violence.
"Three of the alleged incidents disclosed to me in interviews were in my view extremely serious and some appeared to be part of a multi-year pattern of predatory behaviour," Francis said in the report.
This morning, Mallard said his reading of the report was that the three incidents were the actions of one man who was still working at Parliament.
"Reading the report carefully, I get the sense that the man is still on the premises," he told Morning Report.
"I'm not aware whether they are an MP or staff ... I don't know who it is. If I knew who it is, I would tell the police."
He characterised the alleged incidents as rape.
"We're talking about serious sexual assault. Well that, for me, that's rape."
Asked if he meant that people had been raped at Parliament, he said: "That is the impression I get from the report, yes."
National deputy leader Paula Bennett told media that police should be involved immediately, given Mallard's comments this morning.
"It has led many to believe that there is a rapist on our premises currently working here.
"There are people here that are feeling unsafe at the moment. I personally am dealing with staff that are feeling very vulnerable and upset, and describe themselves as feeling ill and uncomfortable and nervous."
"Debbie Francis does. She was contracted by [the Speaker]. Something else needs to happen."
Bennett said she did not know who the offender is, nor had anyone from her party come forward to say they had been victims of alleged offending.
"There is a duty of care for Debbie Francis and the Speaker to have police involved immediately so those allegations can be followed up, and the safety of the people working here can be put first.
"For me, it almost feels like they are harbouring a criminal ... This is not just a bit of inappropriate behaviour. The Speaker is alleging a very serious criminal act. I'm not convinced that everything is being done that should be."
Bennett said she was not necessarily calling on Francis to breach the conditions of her contract and name alleged offenders to police. She said the first step was for Mallard to clarify what he knows, and then seek advice from police.
Asked if Parliament was a safe place for women, Bennett said: "It doesn't feel like it today."
Peters was not in the meeting with Ardern because he was meeting Vanuatu's Prime Minister Charlot Salwai, but he said the offender was not someone who worked for any political party.
"It's not a parliamentarian and it's not a parliamentary staffer, so all the parties are clear on this matter ... so that leaves just the system itself."
It is unclear what Peters meant by "the system".
He would not say what he was basing that on except to say "it's what I know".
He said he did not know who the offender was.
Peters said Mallard's comments this morning were "absolutely repugnant, not correct in any way, shape or form, and we're not going to sit back here and take those sorts of allegations".
He said Mallard should not make such statements without evidence.
"To sheet the evidence home, you've got to have a complainant. Frankly, when you're going to make statements like that, you better know the processes of the law. I'm very unsatisfied with what I've heard."
National MP Judith Collins, who is a former Police Minister, said police did not need a complainant to investigate.
"I think people would like to know. Certainly a lot of the men working here would like to not have themselves being smeared by this.
"I would have thought, if there is evidence at that level - so much so that there is a report of three sexual assaults, apparently by one person - that that matter should go to police, if there is any idea about who this person is."
She did not know who the person was but said she would be surprised if it was an MP.
Mallard said "no comment" to reporters following the meeting with Ardern.
Earlier this morning he said he hoped that victims were being supported by the proper agencies and would make a complaint to police if they wanted to.
"Clearly it's an intolerable situation, and that's why we're working very hard.
"Each of the chief executives of the different agencies, each of the party leaders, has been encouraging women who have been sexually assaulted, or assaulted in any way, to go to the support agencies who can support them with a complaint to the police."
The review went back as far as 2014, but Mallard said that the complaints could have been about earlier incidents because the review had allowed that.
Yesterday, Francis declined to comment on whether any police investigations had been launched as a result of the review, in which all respondents are anonymous. She said her review was not aimed at investigating specific incidents but rather patterns of behaviour.
A police spokesperson said they would not confirm or discuss any matters which may have been raised with them as a result of the review process.
"We encourage anyone who wishes to discuss matters of concern with the police to contact us. You will be treated professionally and with empathy while we assess any information which may be provided," the spokesperson said.
Francis' independent review showed there is virtually no part of Parliament that is untouched by a toxic culture, painting a grim picture of working in the country's heart of democracy.
Staff and MPs alike told similar stories to Francis, who received more than 100 written submissions, carried out more than 200 interviews and 42 focus groups from December last year to March this year.
Of the more than 1000 respondents, 29 per cent had experienced some form of bullying or harassment from either an MP or a manager, 30 per cent from peers and 24 per cent from a member of the public.
Some 56 per cent had experienced destructive gossip, 47 per cent demeaning language, 53 per cent a lack of co-operation and support and 41 per cent aggressive behaviour.
Francis found there was a known minority of MPs whose conduct was unacceptable.
"The fundamental problem is the power imbalance. It's a master-servant relationship and they're treated like gods. While they are due our respect, they are not god," one respondent said.
Francis said Parliament should invest in a range of protective factors that reduced the risks of bullying, harassment and other adverse behaviours.
She made 85 recommendations, including explicit investment in the development of a culture of dignity and respect; additional investment in leadership development; better pastoral care; greater investment in strategic workforce management and a shake-up of HR; better health, safety and wellbeing policies, processes, engagement and governance, removal of barriers to disclosure; and ongoing monitoring, evaluation audit of the cultural health of the workplace.
