NSW’s deputy leader has accused the WA Premier of being “offensive” as a war of words between the two men continues.

Deputy Premier John Barilaro stepped in as temporary NSW leader last week and soon got in a spat with WA Premier Mark McGowan over the two states’ COVID-19 response.

The tit-for-tat has continued even after Mr Barilaro was relieved as leader.

He reacted strongly on Tuesday morning against a suggestion by Mr McGowan that NSW take inspiration from other states that have “eliminated” the coronavirus, in the sense of stopping community transmission.

“The idea that you tick along with the virus and somehow that is a better model is wrong,” Mr McGowan told reporters on Monday.

“I just urge the NSW government and people in NSW to look outside of NSW at what other states and territories are doing in order to crush and kill the virus.”

The WA Premier said Queensland “did the right thing” to lock down Brisbane for three days following a community transmission event, going on to suggest: “It would be, I think, advisable if NSW eliminated the virus from Sydney and that would of course mean that we could rest a lot easier across Australia.”

In an interview with the 2GB radio station, Mr Barilaro said he was “happy” to “have a go straight back at” Mr McGowan.

“It’s offensive, it was never about elimination. We know we can’t eliminate it. It’s suppression, it’s about no community transmission,” he said.

“Victoria has had problems, Queensland has had problems. For Mark McGowan it’s easy, he puts up the borders in WA, cuts himself off from the rest of the nation … Jeez, here he is again lecturing.”

Mr Barilaro said Mr McGowan would have to “stand for” death and suffering that would come as a result of social isolation.

“Stop lecturing us, and look after your own backyard,” he said.

Mr Barilaro’s comments came after he revealed two of his relatives died in Italy last month from COVID-19 complications.

“2020 was a year that I think the Barilaros would like to seal and forget … It’s been a tough year,” he said.

Mr Barilaro also lost his father last year and at one point took a mental health break from politics after threatening to blow up NSW’s Coalition government over an internal disagreement on koala protections.

The NSW government was backed up on Tuesday morning by Deputy Prime Minister Michael McCormack.

“I don’t think that he should be criticising Gladys Berejiklian,” Mr McCormack said of the WA Premier on ABC’s News Breakfast show.

“I think, instead, (he) should be picking the phone up and saying – thank you for doing what you’ve done and NSW has been very, very good at keeping its economy open and helping not just its own state but all of Australia.”

WA has a hard border in place with NSW, which means the limited amount of people allowed to enter the state have to apply for a permit and then self-isolate for a fortnight.

Monday marked nine months of no community transmission in WA.

NSW, which is responsible for quarantining the vast majority of returning overseas travellers, including those who then continue on to other states, has had a tougher time containing the virus.

The state has logged at least 177 local infections since a current outbreak began in Sydney last month.