An American tourist and a safari guide kidnapped by gunmen in a Ugandan national park have been recovered safe and sound after a ransom was paid for their release, a safari firm said on Sunday.

Police spokeswoman Polly Namaye, who did not confirm the ransom payment, credited the safe recovery of the pair "to the untiring efforts" of the search teams who were drawn from the police, military and the wildlife authority.

"The victims of last week's kidnapping have been recovered alive," Namaye said.

Mike Walker, manager of Wild Frontiers Safaris, said US tourist Kimberly Endicott and the guide, named only as 'Jean-Paul' by a government spokesman, were "back safe".

"Ransom paid and people exchanged," he told AFP by text.

Mr Bashir Hangi, the Uganda Wildlife Authority (UWA) spokesperson, on Sunday told Daily Monitor that the abductees had been found before promising to provide more details later.

"[It's] true, details to follow later," Mr Hangi replied to a WhatsApp message from this reporter.

Four kidnappers stopped a group of tourists at gunpoint around dusk on Tuesday as they drove through the Queen Elizabeth National Park on safari to see wild animals.

Queen Elizabeth National Park, one of the East African nation's most popular wildlife reserves, runs along the border with conflict-wracked regions of the Democratic Republic of Congo.

It borders the famous Virunga national park, the oldest in Africa.

Government spokesman Ofwono Opondo wrote on Twitter that Endicott and Jean-Paul, were rescued "by Uganda security forces in the DRC".