The local MP who covers Coatbridge, Chryston and Bellshill, made the comments at a Labour students’ event.
His party have now arranged for him to undergo equality and diversity training following the comments about the LGBT community and Chinese people.
The Scottish Labour group said Mr Gaffney had been reprimanded for what the MP himself had said was “deeply offensive and unacceptable comments.” The SNP have called for him to be suspended from the party.
Mr Gaffney said: “Last week I attended a Labour Students Burns Supper in Edinburgh.
“At that event I used certain language relating to the Chinese and LGBT communities that was wrong and completely inappropriate.
“I want to offer my unreserved apologies for what I said, my remarks were deeply offensive and unacceptable.
“I will be taking part in equality and diversity training at the earliest opportunity.
“I will do everything possible to make amends with both the Chinese community and the LGBT community.
“I would also like to apologise to the people of Coatbridge, Chryston and Bellshill for any embarrassment this has caused them.”
Humza Yousaf tweeted: “This is utterly awful. A simple apology and diversity training does NOT cut it! In fact it is a slap in the face to suggest this absolves him.
“Hope @LabourRichard takes serious action against Hugh Gaffney. At very least he should be suspended from the party and whip withdrawn.”
Scottish Labour leadership contender Anas Sarwar has claimed he was subjected to racial abuse during his campaign.
He also took to Twitter to make his feelings known, saying: “Today is sadly another example of why we need to recognise that everyday racism is a reality. I published an 8-point plan yesterday on how @scottishlabour can lead by example.... Deeds not words.”
SNP Councillor for Thorniewood, Steven Bonnar, has called on North Lanarkshire Labour leader Councillor Jim Logue to suspend Hugh Gaffney from the Labour group.
Commenting, Councillor Bonnar said: “I was disgusted to read about these comments in the media and the Labour leader in North Lanarkshire must take swift action to suspend Councillor Gaffney from his group while the matter is investigated.
“Councillor Gaffney should take time to consider himself if his comments are compatible with representing the people of Thorniewood as a councillor and the people of Coatbridge, Chryston and Bellshill as their Westminster MP.
“It just isn’t good enough to suggest that attending a training course makes these comments somehow more palatable. Comments such as these have no place in modern Scotland and I find it difficult to see how Councillor Gaffney can conceivably continue as an elected member representing such diverse communities.”