Relatives of more than 40 illegal workers say there is little chance of saving them.
Zimbabwe erupted in violent protest after the government doubled the price of petrol.
Opposition figures are in hiding as arrests and beatings continue. But the anger at Mnangagwa’s regime persists.
The opposition says hundreds of people have been arrested and many more beaten and tortured by security forces.
The country's largest mobile operator - Econet - says it's been ordered to shut services until further notice.
The president said that the oil exploration project is in partnership with Australian energy company Invictus.
KFC has closed its local outlets citing "these difficult times," while supermarkets have been rationing some items.
KFC put up notices at its branches in the capital, Harare, and the second city, Bulawayo, saying they would remain closed "during these difficult times" until further notice.