President Cyril Ramaphosa on Thursday said he had appointed two special envoys to go to Harare "following recent reports of difficulties that the Republic of Zimbabwe is experiencing".
Mnangagwa took over from long-time ruler Robert Mugabe after a coup in November 2017 and many Zimbabweans complain that the country's situation has only gotten worse since.
The Zimbabwean government has dismissed allegations of rights abuses and a crisis in the country as "false".
"There is no crisis or implosion in Zimbabwe. Neither has there been any abductions or 'war' on citizens," government spokesperson Nick Mangwana said in a statement.