The Australian Capital Territory opposition leader has demanded the resignation of the education minister, Joy Burch, for retweeting a comment that her federal counterpart, Christopher Pyne, was a “cunt”.

Jeremy Hanson said Burch was no longer fit to remain in charge of the education of ACT children and the incident threatened to undermine her ability to negotiate effectively with the Commonwealth.

Burch has apologised for retweeting the comment that another Twitter user made after a fiery meeting between Pyne and state and territory education ministers over school funding last Friday.

That night, a Twitter user, @GhostOfPJK, posted a photo of Pyne watching a media conference of five state and territory education ministers who were demanding the federal government honour its promise to match school funding agreements struck before the election. The tweet said: “As the NSW education minster rails against the #gonski betrayal … #pyne is smugly loitering. What a cunt. #auspol”

Burch said she had retweeted the comment accidentally, removed it swiftly and contacted Pyne’s office to say sorry. “I sincerely apologise for any offence it may have caused,” she said in a statement. Burch – whose portfolios in the ACT government include education, training, disability and young people – also argued in the Canberra Times that it was a mistake owing to her poor social media skills.

Hanson said Burch had demonstrated “incredibly poor judgment” to retweet the highly offensive description of her federal counterpart.

“It’s unacceptable for Joy Burch to be in charge of schools and the education of children in the ACT. She’s no longer fit to serve,” he said in a statement issued on Friday. “To be the minister for education, high standards have to be adhered to, including the ministerial code of conduct which requires ministers to act with ‘respect for others’.

“If I or Christopher Pyne had used the same abusive language describing Joy Burch, there’d no doubt be uproar in the media. How can this be acceptable behaviour from a minister in the ACT government?”

The meeting last Friday was the first post-election gathering between Pyne and all state and territory education ministers. Jurisdictions that had already signed deals with the Commonwealth to roll out Gonski-inspired school funding from next year voiced fears they would lose out from a possible renegotiation of funding amounts to include the hold-out governments of Western Australia, the Northern Territory and Queensland. Three days later, the prime minister, Tony Abbott, and Pyne sought to quell the concerns by pledging to spend the full $1.2bn originally earmarked for the three non-signatory jurisdictions for the coming four years.