Senator Molan died aged 72 on Monday surrounded by his family, following a "sudden and rapid" decline in his health after Christmas.

"He was many things - a soldier, a pilot, an author, a volunteer firefighter, and a senator. Most of all, he was an adored husband, father, grandfather, and brother," his family said in a public statement on Tuesday.

"Our loss is immeasurable, but we are comforted in our memories of a full life courageously lived, devoted to family and in service of the country he loved.

"We thank you for your thoughts and prayers, and for respecting our privacy at this difficult time."

Senator Molan, who represented NSW, was a major-general in the army, serving across a 40-year period in Papua New Guinea, Indonesia, East Timor, Malaysia, Germany, the United States and Iraq.

He was diagnosed with cancer in 2021, taking leave from the Senate for treatment.

Opposition Leader Peter Dutton described his colleague as a "soldier's soldier".

"Jim was a distinguished soldier and military commander, an admired politician of centre-right convictions and a perceptive author and respected public commentator who expressed his views with courage," Mr Dutton said.

"Whether it was on the battlefield, in the political arena or on the media stage, Jim was admired for his discernment, leadership and unfailingly courteous manner."

Liberal colleague Hollie Hughes shared details of conversations she had with him before Christmas.

"(We) were having a chat about how it was, he'd finished his chemo, he was feeling better and was waiting to see how it had gone ... we both sort of said, 'Well, that's it, quiet time in January and I'll see you back in February'," she told Nine Radio.

"It's just such a sad, sad day, he's going to be greatly missed, not only by the country and the contribution that he made, but our Senate team is very, very close."

Prime Minister Anthony Albanese sent condolences to his family and friends.

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"Jim Molan lived his life in service of our country ... he was a man of principle and a politician of conviction," he tweeted.

Former prime minister Scott Morrison said he left "an amazing legacy".

"He was a very big man, Jim - big in stature ... he had big ideas, he had big passions," he told Nine Radio.

Senator Molan was re-elected to the Senate at the 2022 federal election.

Defence Minister Richard Marles paid tribute to his exemplary military service.

"We're obviously on opposite sides of the fence but we both shared an interest in national security ... he was an honourable and gracious man and having served in the Senate for five years, he's been a fierce advocate for our nation," he told Nine Radio.

Former RSL president and army veteran James Brown said Senator Molan was a "great patriot".

"A deep thinker, an unstoppable force, and a good friend - we will miss him."

His replacement in the Senate is likely to be held up by the NSW state election in March, as it requires the selection of a nominee by the Liberal party and the endorsement of a joint sitting of the state parliament.

Australian Associated Press