South African police have rescued a kidnapped American pastor "miraculously unharmed" following a deadly shootout, authorities said on Wednesday.

Josh Sullivan, 45, was seized by armed men last week as he led a prayer service at his church in Gqeberha in the Eastern Cape Province. He was rescued in the same city on Tuesday, South Africa's elite police unit Hawks said in a statement.

Three suspects were killed during "a high-intensity shootout" as law enforcement officers approached a vehicle at a location where Sullivan was being held, police said.

"The victim was found inside the same vehicle from which the suspects had launched their attack. Miraculously unharmed, he was immediately assessed by medical personnel and is currently in an excellent condition," police said.

High levels of poverty and inequality have created fertile ground for crime to take root in South Africa, with a proliferation of criminal gangs and illegal weapons fueling a rise in kidnappings for ransom.