Mr Mnangagwa made the comments on Thursday during a one-day visit to Mozambique, New Zimbabwe news site reports.
He said that he had a telephone conversation with the 93-year-old leader who asked him why he was out of the country.
He recounted the conversation while mimicking Mr Mugabe's voice:
Emmerson. Where are you? 'In South Africa'. What are you doing there? 'You fired me...you fired me last week."
A video of his remarks has been shared on YouTube:
Mr Mnangagwa said that Mr Mugabe then urged him to return to Zimbabwe, but says he replied that "there are people who surround you want to eliminate me".
He said he feared for his life.
Behind the scenes, Mr Mnangagwa had been involved in an intense campaign against First Lady Grace Mugabe to succeed Mr Mugabe as president.
He was subsequently fired as deputy vice-president leading the military to launch a dramatic takeover which ended Mr Mugabe's 37-year rule.
Mr Mnangagwa returned to the country from South Africa and was sworn in as president on 24 November.
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