On Saturday night Mr Alexander, while standing next to a beaming Prime Minister, Malcolm Turnbull, told a story about someone who had come up to tell him that he had built Tennis World, a tennis complex.

Mr Alexander said that when he thought his tennis career was over, his back improved when he started coaching at the centre.

"Then I got to about No.14 in the world," said Mr Alexander, who will be returning to Parliament as the holder of a seat he first won in 2010.

"The doctor at the time said, 'You have eligibility for a disabled sticker'. I said, 'I still have some pride,'" Mr Alexander said. "That was before I entered politics."

The comment drew ire from those who interpreted it as offensive to the disabled.

"I think it is inappropriate because it is suggesting that the use of a disability parking sticker is in some way inferior," said Graeme Innes, the former Disability Discrimination commissioner.

"The use of a disability sticker is what some of us need to do to compensate for our disability and some of us are quite proud to be people with disabilities, doing what we do," said Mr Innes, who is blind.

Back alongside Mr Turnbull at a press conference on Sunday morning, Mr Alexander apologised while also emphasising he had not meant to cause any offence.

He also highlighted work he had done in the community with organisations that offer services to people with a disability, such as Ryde Rehab and Achieve Australia.

"You can be mischievous with the interpretation, what I was saying was that nobody who doesn't have the right ... to have such a parking sticker should take it," he said.

"If anybody has been offended, I apologise, the point was that no one should take a disability sticker who shouldn't have it or who doesn't deserve it."

Mr Turnbull backed his newly returned MP and said Mr Alexander "respects everybody in this community, and he shows real leadership, particularly in the area of disability services".

"John has already said that those people who were offended, he apologises. John is a great Australian with a big heart."

The byelection was triggered by the discovery Mr Alexander was a British citizen, in contravention of the constitution.

"To the people of Bennelong it has been regrettable that we had to go through this experience, that we had to have a byelection," said Mr Alexander, before dubbing the victory a "renaissance" of Mr Turnbull's leadership.

"It has been a most unifying and humbling experience."

Mr Innes said that, regardless of what Mr Alexander may have been trying to convey with his comment, politicians could only be judged on what they said.

"Why make a joke about a thing like that, which, for a person who needs a sticker like that is a serious issue," said Mr Innes.

Labor's disability spokeswoman, Carol Brown, had earlier called on Mr Alexander to apologise.

"To suggest that Australians who require a disability parking permit have anything to be ashamed of is repugnant," Senator Brown said.

As a tennis professional, Mr Alexander rose to No.8 in the world.