Mr Burns said he and the other politicians told the group to leave, but one of the "henchmen turned his back on my and shielded Mr Chapman from anything I was attempting to say".
"After about two to three minutes they turned around and marched back out again."
He said it had been a "very civil" election meeting up until that point, and the demonstration came as a shock to many in the audience, particularly older people.
"It was pretty scary for some people for the time that they were there.
"It was pathetic and I think that is was designed to intimidate."
Mr Chapman disputed that people were threatened.
"The older people in that meeting were getting quite boisterous towards us, in fact there was some of them that were heckling us. I don't remember seeing anyone that was openly scared.
Mr Chapman said it was necessary for the group to be wearing fatigues and balaclavas, otherwise the media would not be interested in the demonstration.
He said the aim of the action was to publicise issues the ground want to be addressed.
"The only way we could do that was to do a publicity stunt that would get media attention.
"The rising poverty in New Zealand and the suffering population amongst the lower class is going to create a situation in the future that is not going to be pretty for New Zealand.
We just want to wake up the Government who are obviously too stuck in their own high salaries to realise that other people in this country are suffering. So it is time that somebody told them."
Mr Chapman said last night's demonstration was the first by the group ahead of Saturday's election, but there would be more in the future.
However Mr Burns said disruptive demonstrations like the one last night are not appropriate.
"I believe if someone like him wants to have a political voice, he should do what everyone else who wants to have a political voice does and stand for parliament rather than gate-crashing a political meeting and trying to impose his views in bully boy style.
"Of course he has stood twice for the Christchurch Mayoralty with a spectacular lack of success."
Mr Burns said despite the perception that Christchurch has a problem with white-supremacists, groups like Right Wing Resistance are active around the country and not exclusive to Christchurch.
"I think the fact that Chapman lives here and is a self-styled leader of the thing probably gives it a little bit more profile here.