Grey Power is enraged by what it says is the stupid and dangerous behaviour of people fleeing managed isolation facilities, and says they need the book thrown at them.
A person broke a window and absconded from the Waipuna Hotel in Auckland on Friday, the fourth such escape in a week.
The person was picked up by police about an hour later and tested negative for Covid-19 in their day-three test.
Earlier this week a man who was later found to have Covid-19 left an Auckland isolation facility and went to a nearby supermarket.
Grey Power president Mac Welch said the shocking conduct risked spreading Covid-19 into the population - with older people particularly vulnerable.
"They're playing with people's lives, they're playing with all the hard work that the citizens of New Zealand put into containing [Covid-19] and beating it," Welch said.
"It is just so wrong, it infuriates me and I'm sure it infuriates a hang of a lot of other Kiwis."
Welch said everyone who escapes from isolation facilities needs to be punished severely.
"None of the soft, cuddly touchy rubbish that we keep seeing continuously with these people, they need to be hammered to the full extent of the law.
"If these people, who have been looked after and waited on hand and foot, are going to abuse the privilege - lock them up.
"Don't muck around, lock them up."
People charged under the Covid-19 Public Health Response Act can face either six months' imprisonment or a $4000 fine.
The National Party said the government's ineptitude was putting the public at risk.
Party spokesperson for Covid Recovery Amy Adams said the public were right to expect the government to be able to keep people from getting out of the quarantine hotels.
"It should not be beyond the capacity of the government and public service to do that.
"It is a failure from the top-down and ... despite repeated assurances that they are on to it and things will be different now this stuff keeps happening."
Adams said there needed to be a zero-tolerance approach to any chance of public contamination from any returning New Zealanders.
"We need to do whatever security and whatever restrictions are required for that to happen."