NSW Deputy Premier John Barilaro faces further trouble after letting slip that he spent at least part of the weekend on his farm, more than 100 kilometres from his Queanbeyan home.

NSW police are inquiring into the trip after Mr Barilaro – who has been vocal in leading official calls for people to stay home during the coronavirus lockdown – revealed it at a media conference on Monday.

Explaining he would not contest the federal South Coast seat of Eden-Monaro at a looming byelection, Mr Barilaro said had made the decision after driving almost two hours to his family farm at Nerriga, on the Southern Tablelands at the weekend

“I had the opportunity at the weekend down on the farm to build a cubby house with my four-year-old. I had the opportunity to be fun and silly,” he said.

On Thursday, NSW Police Deputy Commissioner Gary Worboys flagged a possible investigation into whether the journey breached orders to avoid non-essential travel amid the coronavirus pandemic.

“We’ll speak to a number of people about it – whether we commence an investigation or not will rely on that information,” Mr Worboys said.

In a statement on Thursday, the NSW Nationals leader said he went to the farm to “feed chickens, mow lawns and tend to maintenance”.

“In NSW you have always been permitted to travel to your farm or property to tend to it,” he said.

“As of 1 May two adults and dependant children can visit another household, no matter the distance required to travel.

“My property in Nerriga is located within my electorate of Monaro and is an acreage, which requires maintenance.”

But back in March, he urged NSW residents to stay home.

“Now is not the time to travel from metropolitan areas to regional NSW for a holiday, for meetings, or even to relocate yourselves for a longer period – the safest thing you can do right now is stay in your community,” he said.

The Sydney Morning Herald quoted him as say those who lived in the regions must “make the tough call to tell any friends and family in the city you’ll see them at Christmas, no sooner”.

Premier Gladys Berejiklian said she was unaware of Mr Barilaro’s weekend trip.

“I think it’s important for us to acknowledge that, unlike other states, NSW hasn’t put a restriction on how far you can travel if it’s for work, or to care for someone,” she said on Thursday.

NSW Arts Minister Don Harwin resigned in April after it was revealed he had been sprung staying at his Central Coast beach house during the lockdown.

He was also fined $1000 for breaching travel restrictions.

At the time, Mr Barilaro said he was “bloody angry” about Mr Harwin’s conduct.

“What Don Harwin has done over the last couple of weeks is unacceptable. I’m absolutely upset about it,” Mr Barilaro said.

“In the public eye, it looks like politicians believe they’re above the rules and above the law – and we’re not.”

Also on Thursday, Ms Berejiklian refused to be drawn on the ugly spat between Mr Barilaro and her transport minister, Andrew Constance, about the Eden-Monaro byelection.

“All I will outline … is my expectation of every member of the team to keep their head down and work hard,” she said.

Mr Constance announced on Tuesday he wanted to make the move to the federal seat, only to withdraw from the race 24 hours later.

He said he changed his mind after Sydney’s Daily Telegraph reported that Mr Barilaro had used a crude word to describe him to colleagues.

“I hadn’t signed up to contest federally to be called that kind of smear,” Mr Constance, the state member for Bega, said.

Earlier, a text message Mr Barilaro sent to federal Nationals leader Michael McCormack after deciding not to contest Eden-Monaro was leaked to Sky News.

“You have failed your team and failed as a leader,” Mr Barilaro wrote to the deputy PM, accusing Mr McCormack of not supporting his tilt.

There are likely to be two contenders for Liberal preselection when nominations for the South Coast seat close on Friday morning.

The Liberal candidate at the 2019 federal election, Fiona Kotvojs, is the frontrunner. Former Navy seaman Jerry Nockles is also considering contesting.

The byelection follows last week’s resignation of Labor member Mike Kelly, due to ill health.

-with AAP