An Australian deputy chief minister is in trouble for allegedly calling the gay son of another politician a “pillow biter” and “shirt lifter”.

Gary Higgins, the Member for Daly, refused to attend all meetings over alleged homophobic slurs against his son, Joshua Higgins, by Northern Territory Deputy Chief Minister Dave Tollner.

The incident happened during a row over the content of a draft speech.

Joshua Higgins – an aide to Community Services Minister Bess Price – was present during Mr Tollner’s outburst.

Mr Tollner has apologised to Mr Higgins’ son for the comments, which have also been condemned by Chief Minister Adam Giles as “inappropriate” and “not acceptable.”

Calls for Mr Tollner to resign have been rejected by Mr Giles.

“He is aware that I take a hard line against inappropriate language in the workplace and I have let him know that in my opinion, his remarks were not acceptable,” Mr Giles said in a statement to Guardian Australia.

“The treasurer has told me that he did not intend to cause harm or offence with these comments and I know the individual concerned has accepted Mr Tollner’s apology. The person in question is a valued staff member and has met with me and expressed a desire to move on and that’s what we now intend to do.”

In his statement, Gary Higgins said the family had dealt with “similar issues before” and Mr Tollner had his support. “My son and I accepted an apology from Mr Tollner,” he said, adding that he understood he “may have misinterpreted” comments from the deputy chief minister.

Earlier this summer, Mr Tollner was criticised for appearing to mock indigenous Australians.