Prime Minister Jacinda Ardern yesterday flatly rejected the protesters' request for a meeting, pointing out some carried signs calling for the death of politicians.
Heading into a caucus meeting at Parliament this morning, Luxon told media it was difficult to engage with the group given their "anti-social, abusive" behaviour.
"We respect people's right to protest but we expect them do it within the rules - and that's not been happening. We are a party of law and order," Luxon said.
"When you come here to talk about freedoms and then you impinge the freedoms of others ... that's not on."
Luxon said the matter was further complicated by the diverse range of groups and interests involved and the lack of defined leadership.
"They range from white supremacists to Māori separatists and everything in-between ... anti-authority through to anti-vaccination to anti-mandate."
Luxon has temporarily moved out of his Wellington apartment - which is located near the encampment - and boosted his security.
National's Covid-19 Response spokesperson Chris Bishop this morning told reporters the full caucus had agreed not to meet or engage with the protesters.
"Look out the window: You can see signs in chalk that say 'hang 'em high'," Bishop said.
"I don't seriously understand how [protesters] can expect MPs to go and engage with people who want to lynch us."
The opposition National party has strongly backed vaccination efforts throughout the pandemic, but several of its MPs have muddied the waters.
Most recently, Maureen Pugh published a Facebook post thanking the Convoy protest movement, but then deleted it, saying she was unaware of the group's anti-vaccination messages. Harete Hipango was also criticised after attending two anti-mandate protests.
Luxon said all his MPs were "pro-vaccination, pro-boosters".
"Everybody's been very clear about that," he said. "That's what all of us believe."
Former police lead crisis negotiator Lance Burdett yesterday encouraged government representatives to meet with the protesters in a neutral venue to hear them out.
"There are plenty of opportunities to come together. It's just having one person from one side making the first move."
The suggestion was roundly rejected by Ardern: "What I have seen down on that forecourt does not suggest to me that this is a group that are interested in engaging in policy development.
