In an emotional press conference on Thursday, he said the decision to resign was "gut-wrenching".

"I really do regret [resigning], and it has broken my heart to do this," he said.

"I wouldn't be doing it if it just wasn't absolutely necessary to do it."

Dr Kelly has undergone 10 surgical procedures in the past six months, linked to renal issues sustained during his time in the military after becoming severely dehydrated.

He also revealed the Department of Veterans' Affairs classified him as permanently impaired due to deteriorating osteoarthritis.

"[Eden-Monaro] is 42,000 square kilometres of rough terrain, difficult weather, incredibly diverse, incredibly challenging, where the community that is spread out and really requires you to be out on the road a hell of a lot," he said.

"And I just can't do that physically any more."

Dr Kelly won the seat in 2007 before losing it at the 2013 election and regaining it in 2016.

Labor leader Anthony Albanese has paid tribute to Dr Kelly's service in the parliament, calling him an extraordinary Australian.

"He has brought a great deal of dignity, talent, capacity and commitment to this parliament," he said.

"He perhaps has downplayed how tough the last six months have been for him.

"Every time I have spoken to him, even on the days where he is about to undergo a procedure, he has focused on the people of the electorate of Eden-Monaro."

The resignation has fueled speculation NSW Deputy Premier and state member for Monaro John Barilaro will run for the seat.

Mr Barilaro said he was weighing up his options and would use coming days to decide whether he would put his hand up.

"I had said I would never run against Mike Kelly, but now there is a vacancy I will consider it," he told ABC radio on Thursday.

"I'll take the weekend to think about it; I'll have to speak with the family."

While he said the prospect of working closer to his home in Jerrabomberra was enticing, Mr Barilaro said he wouldn't want to let NSW Premier Gladys Berejiklian down by resigning from NSW parliament to contest the by-election.

Bega mayor Kristy McBain has been tipped to run for Labor.

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While it has been 100 years since a government took a seat off the opposition at a by-election, Mr Albanese said the Coalition would go into the poll as favourites.

The Opposition Leader said the recent bushfire crisis and the response to it would be a key issue at the by-election.

NSW Bega MP Andrew Constance and former Liberal senator Jim Molan have also been possibilities to run for the seat.

Mr Barilaro said he would not run against Mr Constance, whom he considered a close friend.

"I don't believe a three-corner contest [between the Nationals, Liberal and Labor] will serve us well," he said.

Prime Minister Scott Morrison is talking down the prospect of claiming control of a marginal seat despite a hot field of potential Coalition candidates.

Mr Morrison confirmed on Wednesday the Liberal Party would contest the seat and expected the Nationals would also run a candidate.

But he said it would be a once-in-a-100 year event for a government to pick up an opposition seat at a by-election.

"That would be a rather extraordinary outcome but it's one we will put our best foot forward for in this environment," Mr Morrison said on Wednesday.

The seat had long been considered a bellwether of federal elections - the party who won the seat won government - but lost that status at the 2016 election.

The previous Liberal candidate for the seat, Fiona Kotvojs, said she would put her hand up to run in the by-election.

While she said there hadn't been any formal contact with party headquarters at this stage, she hoped the pre-selection would be a strong contest.

"[The electorate] want a good candidate who will work hard for the electorate and who is committed," she said.

The former federal candidate also said a two-way contest would be preferable to having the Nationals run a candidate in a three-way race.

"It's a decision for the Nationals to make," Ms Kotvojs said.

"A three-way contest is complicated and creates more confusion."

News of Dr Kelly's resignation has triggered tributes from his federal colleagues.

Former Labor leader Kevin Rudd said he had a "deep appreciation and respect" for the Eden-Monaro MP, who was first elected in 2007 when Mr Rudd became prime minister.

"[He was] a person of great personal and professional integrity, he is a great loss to the parliament and the Labor Party," he wrote on Twitter.

Shadow attorney-general Mark Dreyfuss said he was sad to see Dr Kelly leave parliament.

"I'll miss his friendship, his advice and the experience and the humanity he brought to the parliament," he said.

Former senator Doug Cameron described Dr Kelly as "one of the genuine good guys".