"We didn't do it for the sake of entertainment," talk radio station Radio24syv wrote on Twitter.
"Thousands of animals die each day so that people can eat them," it added.
The broadcaster said radio host Asger Juhl on Monday killed baby rabbit Allan with repeated blows to the head to highlight "hypocrisy" in Danes' attitudes towards animal welfare.
"We buy and eat animals that have had an awful life. And animals that have been killed under the same controlled conditions as the rabbit in the studio," it wrote in a statement.
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"They wanted to see if they could kill him during the last show or if they had gotten too attached to him," she said in a video clip on her Facebook page.
Kessler said she thought she was capable of wresting the animal from Juhl but feared it would die a more painful death if she grabbed it.
"I hit it hard over the neck twice so that the cervical vertebrae fractured," Juhl told broadcaster TV 2.
Juhl said he had brought the dead rabbit with him home -- where he had skinned and cut it up with his children, aged six and eight -- and that he later would have rabbit stew for dinner with fellow morning host Kristoffer Eriksen.
A Copenhagen zoo prompted international outrage last year by putting down a healthy giraffe, known as Marius, and then dissecting it in front of children.
That incident, just like the radio station's stunt, drew a mixed response in Denmark where agriculture is a key export industry.
Radio24syv said it wanted to put more focus on "one of the world's most industrialised agriculture sectors."
Danish farming "allows 25,000 piglets to die every day because farming has been streamlined and (breeds) pigs that give birth to far more offspring than the mother pig can handle," it said.