NSW Transport Minister Andrew Constance has abandoned his bid to enter the federal Parliament less than 24 hours after announcing he would seek Liberal pre-selection at the Eden-Monaro by-election.

Mr Constance, whose state electorate of Bega overlaps the federal division of Eden-Monaro, was seen as a strong candidate.

In a statement, Mr Constance said: "I need to remain focused on the bushfire recovery and be grateful for the opportunities I already have."

He also said he had "unfinished business" as Transport Minister.

"I appreciate people will be confused by my actions over the past couple of days, and for that I am sorry," he said.

Labor's Mike Kelly holds the seat on a 0.9 per cent margin but resigned last week for health reasons, sparking a by-election.

A date for the vote has yet to be announced, with coronavirus restrictions predicted to cause a delay.

When asked about her Transport Minister's future, NSW Premier Gladys Berejiklian this morning said: "Can I just stress, the Member for Bega, Andrew Constance, hasn't yet been endorsed as the candidate."

Yesterday, Mr Constance said he believed he had a winning chance thanks to his experience in state politics.

Mr Constance held the position of NSW Treasurer before taking on the transport portfolio.

"People just want someone who can give it a go and I think I can bring something special given that state-wide experience," he said.

He has held his seat of Bega for 17 years but rose to national prominence last summer for his regular public appearances during the bushfire crisis.

Earlier this week, NSW Deputy Premier John Barilaro confirmed he would not contest the by-election for the Nationals.

Both men had previously pledged not to run against each other.

Mr Barilaro confirmed he would still not run, despite Mr Constance's change of heart.

After he withdrew from the pre-selection race, text messages sent by Mr Barilaro to Deputy Prime Minister Michael McCormack, the federal Nationals leader, were leaked to the media.

"Don't hide behind the 'members will choose the candidate' rubbish, as you were the only one saying such lines," Mr Barilaro wrote.

"Don't you think my branches would have backed me in?

"To feel threatened by me clearly shows you have failed your team and failed as a leader.

"The Nats had a chance to create history, to change momentum, and you had a candidate that was prepared to risk everything to make it happen.

"What did you risk? Nothing.

"Hope you are proud of yourself."

Labor endorsed Bega Valley Mayor Kristy McBain as its candidate on Monday.