War veterans, traditional allies of the ruling party have joined in the criticism, saying Zimbabwe doesn’t belong to a family.
Zimbabwe’s main opposition Movement for Democratic Change (MDC) party has accused first lady Grace Mugabe of attempting to create a Mugabe dynasty.
There has been widespread reaction to Grace Mugabe’s call for her husband to name a successor.
She said last week that the president’s word on the matter would be final.
In a statement, MDC spokesman Obert Gutu says his party is seriously concerned by the comments, which he said looked like attempts to openly create a Mugabe dynasty.
War veterans have joined in the criticism.
Secretary General Victor Matemadanda told online website 1st TV that Zimbabwe doesn’t belong to a family or a favoured few.
War veterans are believed to back Vice President Emmerson Mnangagwa to succeed Mugabe.