The remark, implying Cabramatta MP Tri Vo was a service worker, was made during question time in the NSW parliament on Wednesday when the rookie MP was poised to ask a minister a 'Dorothy Dixer' question.
Women's Minister Jodie Harrison told the parliament shortly after Mr Coure had "made an offensive racist comment", and asked that it be withdrawn.
"There is no place for racism in this place," she said.
Mr Coure, who was the multiculturalism minister in the Perrottet government, later apologised for what he said was "a poor attempt at humour and was not intended to cause any offence".
"I withdraw the comment once again and apologise to (Mr Vo)," he said.
"As a former member for multiculturalism, I celebrate our diversity in our society is our greatest asset."
Labor later issued a statement from Mr Vo saying the comments were in poor taste.
"But that's not going to deter me from doing my job and representing my community of Cabramatta," he said.
"That's what I intend to do - continue to be a strong voice and advocate."
Treasurer Daniel Mookhey said it was up to all all MPs to ensure the culture of parliament improved, describing the comments as "inappropriate and offensive".
"I have had people in parliament deliberately mispronounce my name. It is not pleasant. It is offensive," he told reporters.
"As a parliament, we should do better."
Last year, the landmark Broderick report into the culture at NSW parliament found one in three staff were bullied, and one in five had been sexually harassed.
Greens MP Jenny Leong called for Mr Coure to extend his apology to all members of the lower house, saying his comments had caused offence to "many" people in the parliament.
"There is no place for that kind of racist comment in the chamber."
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