The US dentist who killed Zimbabwe's Cecil the lion has broken weeks of silence, saying in an interview that he had no idea it was a special feline and announcing he would return to work after lying low.

In his first interview since sparking international outrage over the killing of the black-maned lion, Walter Palmer told the Minneapolis Star Tribune that he would be back at his dentistry practice on Tuesday.

The skilled trophy hunter said that he and the others in his party had no clue that the lion they were hunting was the revered feline that has been a well-known attraction at the Hwange National Park, according to the paper.

The 55-year-old also maintained in the interview published late Sunday that the July hunt, during which he was armed with a bow and arrow, was legal.

Palmer declined to say whether he would abide by any request to return to Zimbabwe over legal allegations, and an attorney present for the interview added that there had been "no official allegations that he's done anything wrong."

Zimbabwe has asked the United States to extradite Palmer to face charges over the hunt.

The dentist also tried to put to rest what he said had been false information in the media, stating that he had not paid $50,000 to participate in the hunt, without specifying the sum paid.

Palmer said the ordeal had been particularly difficult for his wife and daughter, who had been threatened on social media.

"I don't understand that level of humanity to come after people not involved at all," he said in the article.

He also voiced concern for his employees, stating that he was "a little heartbroken at the disruption in their lives."

"I need to get back to my staff and my patients, and they want me back. That's why I'm back," he said.

Cecil had been wearing a tracking collar as part of an Oxford University research project, but Palmer said he had been unable to see the device in the night and under the animal's mane, adding that it was not illegal to kill lions with collars.

Palmer's guide on the expedition, Zimbabwean Theo Bronkhorst, and Honest Ndlovu, the owner of the land where Cecil was killed, have been charged over the matter in Zimbabwe, where officials allege that they lured the lion out of the park.