The Liberal candidate for a crucial by-election in Sydney that could threaten the Federal Government's majority has apologised after a video of him telling racist jokes emerged.

Key points: John Alexander is a former tennis pro and TV game show judge

John Alexander is a former tennis pro and TV game show judge There are dire consequences if he is defeated at next month's by-election

There are dire consequences if he is defeated at next month's by-election That's because the Turnbull Government would lose its one-seat majority

In the video, which was posted on YouTube in 2011, John Alexander can be heard telling a joke about rape and making racial quips to fellow customers at a Brisbane pub in the 1990s.

The by-election in Bennelong, in Sydney's north, was brought on after Mr Alexander conceded he was "most likely" a dual citizen and therefore ineligible to sit in Federal Parliament.

At one point, he starts a joke: "A black guy in Chicago has witnessed a rape ..."

Mr Alexander said the jokes were told at a wrap party at the end of filming the 1990s TV show Gladiators, which pitted members of the public against a team of gladiators in physical challenges.

"The jokes were crude. When I saw them this morning, I was horrified at my language and I apologise … for the language and the jokes."

In a written statement earlier, Mr Alexander said his jokes were "completely unacceptable".

"More than 20 years ago I told crude and inappropriate jokes, which were completely unacceptable and I apologise unreservedly," he said.

"There is no place for jokes about violence against women. Again, I apologise unreservedly."

Set to be held on December 16, the Bennelong by-election looms as crucial for the Turnbull Government, which would lose its majority if the seat falls to Labor.

Bill Shorten and Kristina Keneally were campaigning in Eastwood today. ( ABC News: Sarah Hawke )

Mr Alexander won Bennelong at last year's federal election on a 9.7 per cent margin, but faces a strong challenge from Labor's candidate, former New South Wales premier Kristina Keneally.

The candidates have been campaigning furiously in the electorate since last week, but it has not been smooth sailing for either.

At her campaign launch on Sunday, Ms Keneally complained about the closure of a Medicare branch, despite it being later revealed it was a Labor Government policy to shut it.

On Monday, Mr Alexander tweeted a photo of himself making phone calls with volunteers, but none of the handsets were plugged in.

John Alexander has apologised 'unreservedly' in a statement. ( AAP: Lukas Coch )

Prime Minister Malcolm Turnbull said Mr Alexander's apology was a "measure of the man".

"Not all disrespect of women ends up in violence against women but that's where all violence against women begins, so all of us need to reflect on that," Mr Turnbull said.

"John has done so."

Speaking in Eastwood, where he was campaigning with Ms Keneally, Labor leader Bill Shorten said:

"The comments are crass, they're wrong, they're stupid, and the apology is 22 years too late."

He said Labor had not dredged up the video to damage Mr Alexander's campaign.