US authorities launched an investigation on Thursday into the killing of a beloved lion in Zimbabwe, as the US dentist who hunted the big cat remained in hiding amid mounting global outrage.

Trophy hunter Walter Palmer killed Cecil the lion earlier this month after the feline was allegedly lured out of the Hwange National Park boundaries with a dead animal as bait.

The professional Zimbabwean hunter who organized the hunt has been charged in Zimbabwe with "failing to prevent an illegal hunt". But a court hearing for the landowner accused of allowing the hunt was delayed on Thursday.

The US government, meanwhile, has opened a probe into the hunt.

"The US Fish & Wildlife Service is investigating the circumstances surrounding the killing of Cecil the lion," said Edward Grace, deputy chief of law enforcement at the agency.

But Palmer remained out of the public eye, and US authorities said they have had no luck so far in their efforts to track him down.

"Multiple efforts to contact Dr Walter Palmer have been unsuccessful," Grace said.

"We ask that Dr Palmer contact us immediately."

Crowds left plush toys of lions, tigers and monkeys at his River Bluff Dental practice in Minnesota. A sign reading "Rot in hell" was plastered on the office door.

More than 100,000 US citizens on the White House website urged the government "to fully cooperate with the Zimbabwe authorities and to extradite Walter Palmer promptly."

A Minnesota congresswoman joined calls to investigate the dentist, a seasoned hunter with a poaching conviction over the 2008 killing of a black bear in the United States.

"To bait and kill a threatened animal, like this African lion, for sport cannot be called hunting, but rather a disgraceful display of callous cruelty," Betty McCollum said.

She urged the US Attorney's Office to "investigate whether US laws were violated related to conspiracy, bribery of foreign officials, and the illegal hunting."

Meanwhile, Safari Club International, an international hunting organization that Palmer belonged to, said it also supported a probe and that it had suspended his membership.

On Tuesday, Palmer issued a statement expressing regret at killing Cecil but said he had no idea the lion was protected and part of a study, and that he thought the hunt was legal.