Palmer, a dentist, allegedly paid $50,000 for the hunt earlier this month in which he shot the lion with a powerful bow and arrow at night, close to Hwange national park in the west of Zimbabwe.
Cecil, who had a distinctive black mane, was a popular tourist attraction at the park and was also wearing a tracking collar as part of a University of Oxford research project.
“We are appealing to the responsible authorities for (Palmer’s) extradition to Zimbabwe so that he can be made accountable for his illegal actions,” environment minister Oppah Muchinguri told reporters in Harare.
“It was too late to apprehend the foreign poacher as he had already absconded to his country of origin.”
Palmer, who is also being investigated by the US Fish and Wildlife Service over Cecil’s killing, has apologised and said he was misled by professional guide Theo Bronkhorst.
Bronkhorst, who organised the expedition, was granted bail by the Hwange court on Wednesday after being charged with “failing to prevent an illegal hunt”.
Muchinguri gave a political spin to Cecil’s death.
“Palmer, being an American citizen, had a well-orchestrated agenda which would tarnish the image of Zimbabwe and further strain the relation between Zimbabwe and the United States,” she alleged.
The US imposed sanctions including travel bans and asset freezes on long-ruling President Robert Mugabe and members of his inner circle after 2002 elections which western observers said were rigged.
Muchinguri said that Palmer, Bronkhorst and the landowner were guilty of illegally “poaching” the lion, which was allegedly lured out of the national park with an elephant carcass.
She said Cecil was “an iconic attraction… which we had successfully managed to look after both in terms of conservation and protection from a cub to a fully-grown lion of 13 years.”