The editor-in-chief of Quadrant, Keith Windschuttle, has apologised for publishing an article that said it would have been preferable for the Manchester bomb to be exploded in the ABC’s Q&A studios, saying it was a serious error of judgment.

Windschuttle said the article failed to meet the standards expected by the magazine, which has been published since 1956 and ordered it be deleted from the website.

“The last thing anyone at Quadrant would do is threaten violence to anyone,” Windschuttle said in a letter to the ABC’s managing director, Michelle Guthrie, who had demanded an apology.

“Even though I do not share all of the interpretations expressed in your letter, I accept your assurance about the offence it caused you and your staff. You have my unreserved apology for any concerns it might have given you.”

However, Quadrant has stopped short of sacking the online editor and author of the article, Roger Franklin, who will instead be “counselled”.

Franklin had refused to back down despite almost 24 hours of condemnation for his views.

Windschuttle wrote to Guthrie late on Wednesday after a storm of criticism about the article, including from the communications minister, Mitch Fifield, appearing before an upper house hearing in Canberra on Wednesday.

“I think this constitutes a new low in Australian public debate and the comments are sick and unhinged,” he said.

Quadrant board member Nick Cater also went on the ABC’s The Drum to apologise for what he called a disgraceful article. “I’m deeply embarrassed,” Cater, the head of the Menzies Research Centre, said.

He said Quadrant’s excellent reputation for intellectual rigour had been damaged by the article and the magazine’s editorial processes would be reviewed.

In her letter Guthrie said Quadrant promoted itself as “the leading general intellectual journal of ideas”.

“Those words ring hollow in the wake of last night’s vicious and offensive attack on the ABC, its staff and its program guests,” she said.

“To take issue with our programming and our content is one thing. But to express the wish that, if there were any justice, the horrific terrorist bombing in Manchester would have taken place in the ABC’s Ultimo studio and killed those assembled there is a new low in Australian public debate.”

But after the apology was aired on The Drum and Windschuttle said it would be taken down, the piece remained as the main feature online at 7.30pm on Wednesday.