Chief Minister Michael Gunner said he instructed his wife to take their infant son and flee their home after anti-vaccine protesters shouted his home address during a rally at Parliament House over the weekend.

Mr Gunner, who recently disclosed in Parliament that his home was undergoing security upgrades to help protect him from a “stalking-type scenario”, told ABC Radio on Tuesday that the comments at the rally on Saturday made him “very worried” for the safety of his family.

Video of the rally, which was broadcast to Facebook, showed a man yelling the Chief Minister’s address and suggesting “that’s where the snake curls up at night”.

More than 1000 people attended the rally to protest Mr Gunner’s mandatory vaccine policy, which will require the vast majority of employed Territorians to have both shots of the COVID-19 vaccine by December 24 or risk losing their jobs and being repeatedly fined $5000.

Mr Gunner said he ordered his wife, ABC journalist Kristy O’Brien, and his infant son to leave their home on Saturday.

“I made sure they left the house immediately because you just don’t know what’s going to happen,” he told the ABC.

“And it’s on the internet, so you just don’t know who’s watching.”

NT Police told the ABC they were investigating the matter but did not provide details.

There were no reports of anyone being at Mr Gunner’s residence.

Mr Gunner’s vaccination policy has angered some, however, the NT Government said bookings for the jab surged in the days after the announcement last week.

Mr Gunner has defended his policy, largely seen as the strictest in the country, as necessary to protect vulnerable Territorians.

He also told ABC that he was not concerned about job losses from the policy.

“I’m not worried about that,” he said. “You’re asking me to be worried about teachers who don’t believe in science, health care workers who don’t believe in medicine.

“I would suggest they simply go get the free, safe, effective vaccine, that 80 per cent of Territorians have had a first dose of.”

Mr Gunner also defended his vaccination policy on the global stage, responding to Texas Republican Senator Ted Cruz who criticised the NT Government’s mandatory vaccines on Twitter as “disgraceful and sad” and “COVID tyranny”.

“Vaccination is so important here because we have vulnerable communities and the oldest continuous living culture on the planet to protect … We don’t need your lectures, mate, you know nothing about us,” Mr Gunner’s social media people responded to Senator Cruz via Mr Gunner’s Twitter account.

In an unusual coincidence, Mr Cruz actually had protesters rally at his Houston home in June, with some of them arrested for trespassing. They were protesting against climate change.