The ABC has publicly challenged conservative commentator Chris Kenny to withdraw a defamation case against the broadcaster following an apology from ABC managing director Mark Scott over a Chaser sketch depicting Kenny having sex with a dog.

Kenny, a News Corp columnist, said he had instructed his lawyers to settle the case “as soon as possible” on April 14 when Scott issued a public apology in April for the skit. But a settlement has not been reached.

The NSW Supreme Court found in March the segment was capable of defaming Kenny, a former Liberal Party staffer.

But it struck out one of Kenny’s arguments that a reasonable viewer would have thought he actually had sex with a dog. Kenny’s lawyers appeared in court on Monday to appeal against this decision.

The ABC’s lawyers have given Kenny until next Monday to withdraw his defamation case, saying he will not be pursued for any costs if he does so.

The ABC says in the letter it is confident Kenny will not win the appeal.

Kenny has not responded to requests for comment.

Scott said in his apology: "I have come to the view with the director of television that the ABC should not have put the skit to air.

"Having reviewed the issue, in my opinion it falls short of the quality demanded by our audience and normally delivered by our programming."

“We understand from various media coverage of the Proceedings that your client has stated that an apology from the ABC would have avoided litigation,” the ABC lawyers say in the letter.

“Further, we note that your client has stated in an interview given to Channel 9 on 5 March 2014 that he did not believe that taxpayers should be paying the ABC to defend this matter.”

The ABC offers to pay Mr Kenny’s legal costs until this point and to read out an apology in court.