An American pastor who was kidnapped by armed men during a church service in South Africa last week has been rescued following a "high-intensity shoot-out" that left three people dead, police say.

Josh Sullivan was found unharmed in the township in Gqeberha in the Eastern Cape on Tuesday evening - the area where the 45-year-old was snatched from last Thursday.

There were no immediate details on the kidnappers who are suspected of having been familiar with the family's movements.

Over the past decade, there has been a dramatic increase in kidnappings for ransom in South Africa.

Mr Sullivan's kidnappers had made a ransom demand, prompting the intervention of South Africa's elite police unit, known as the Hawks.

In a statement released on Wednesday morning, the Hawks said that Sullivan had been rescued following "verified intelligence wherein a coordinated team… moved swiftly to the identified location".

Hawks spokesperson Avele Fumba said that as the officers approached the house, the suspects attempted to flee inside a vehicle, while opening fire.

"The officers responded with tactical precision, leading to a high-intensity shootout in which three unidentified suspects were fatally wounded," Mr Fumba said.

Mr Sullivan's family and friends had made impassioned pleas for his safe return since his abduction.

Jeremy Hall, the Sullivan family's spokesman, told local newspaper TimesLIVE that he was at the church with his wife and their children when he was kidnapped.

"They knew his name," he said at the time.

Mr Sullivan describes himself as "a church planting missionary" on his personal website.

On it, he says he moved to South Africa with his wife and children in 2018 to establish a church for Xhosa-speaking people.