Zimbabwe's wildlife authorities have suspended the hunting of lions, leopards and elephants around the country's biggest game reserve following the killing of a much-loved lion by a US dentist.

"Hunting of lions, leopards and elephant in areas outside of Hwange National Park has been suspended with immediate effect," Edson Chidziya, head of Zimbabwe's parks and wildlife authority Zimparks, said in a statement.

The parks body also suspended hunting with bows and arrows, except with permission from the authority's head.

"All such hunts will only be conducted if confirmed and authorized in writing by the Director-General of the Zimbabwe Parks and Wildlife Management Authority, and only if accompanied by parks staff," Chidziya said.

The clampdown follows an international furore over the killing of Cecil the lion, a favourite with international tourists, who was shot with a bow and arrow by Walter Palmer outside Hwange park in early July.

Wanted US dentist Walter Palmer (left) and Cecil the lion (right). (Facebook/YouTube)

The lion, which lived in the park, was lured outside its boundaries by bait.

After shooting the feline, Palmer, who was accompanied by local guide Theo Bronkhorst, then trailed the injured beast for 40 hours before finishing him off with a gun.

The death of the iconic lion, renowned for his distinctive black mane, sparked global outrage, with some animal rights activists calling for Palmer's death.

Bronkhorst is due to appear in court on August 5 on a charge of "failing to prevent an illegal hunt".

Environment Minister Oppah Muchinguri has meanwhile appealed for the United States to extradite Palmer so he can be brought to justice.

Chidziya said the authority had joined forces with the police in a crackdown "to weed out any undesirable elements".