Earlier today, Ardern refused to express a view on the trespass notices, saying it was the Speaker's decision.
However, this afternoon she said she had now spoken to Mallard and encouraged him to speak to other parties and "see if we can come to some consensus on how the issue of trespass notices, and how they apply to everyone, should be issued".
She said it was ultimately a decision for the Speaker, but the meeting of all parties would allow them to discuss how it should be dealt with.
"It is still his call, but I've encouraged him to involve the other parties. He does have the jurisdiction and the responsibility over these grounds, but it is an issue where he's having to decide whether past members of Parliament are treated exactly the same as everyone else is. And I think it's a useful thing for him to discuss with all Parliamentary parties."
Although Parliamentary security had been making the decisions on who to trespass and issuing the notices, Ardern said it was ultimately Mallard's decision.
Former MPs retain some access rights after they leave Parliament and both Peters and King have said they intend to stand in the 2023 election.
Mallard has refused to comment on the issue so far. There were mixed views from other MPs.
National Party shadow leader of the House Chris Bishop said the trespass was a potentially worrying development, and he'd like to know what legal advice Mallard received before the notice was issued.
"It's a pretty extraordinary situation and it has quite deep constitutional implications."
He added: "Winston Peters, I don't like the guy much, but he has been a Deputy Prime Minister on two occasions, one of our longest-running MPs. He just visited the forecourt and he didn't camp out at the protest."
He said one of the questions that needed answering was whether that was different to King's visit, which was as part of the protest.
Te Pāti Māori co-leader Rawiri Waititi had no sympathy for Peters' predicament.
"If he was comfortable to go and be part of the occupation, then you have to reap the consequences of that. So if that's what's come out of this House, he has been banned from two years, well that's got nothing to do with us."
Act leader David Seymour said Mallard was being irresponsible and petty.
"Trevor Mallard doesn't take responsibility when he turns on the sprinklers. Now he won't take responsibility for this. It's always someone else's fault."
Seymour said the Labour Party had been protecting Mallard for a long time.
"He's now got a laundry list of misdemeanours and misbehaviours that always seem to end up costing the taxpayer, as I predict this will."
Seymour said the trespass decision would lead to expensive court cases which would drain public money.
"Trevor Mallard's petulance and pettiness seems to be at the heart of so much drama."
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