"The nation will be advised of the result of talks between the two", he said.
Ruling party Zanu-PF resolved to impeach Mugabe after 37 years at the head of the sub Saharan country.
A draft impeachment motion published by Zanu-PF said the ageing leader was a "source of instability" who had shown disrespect for the rule of law and was to blame for an unprecedented economic tailspin over the past 15 years.
The issue could soon be taken out of Mugabe's hands, with the president's own party expected to set into motion plans to impeach him in the country's parliament Tuesday.
David Coltart, the MDC's secretary for legal affairs, said he supported the move in principle.
Mnangagwa said on Tuesday his desire was to join all Zimbabweans in a "new era" that would rebuild the economy for the benefit of all.
The military was widely hailed as a saviour after effectively stripping Mugabe of his authority last week, but it is under scrutiny after its generals flanked him during a televised address Sunday night in which he asserted that he remained the "commander in chief" and referred to "our well-cherished constitutional order".
Argentina says noise wasn't from missing sub
On Monday, Argentine President Mauricio Macri visited the Mar del Plata naval base to talk with the family members gathered there. The noise was heard in the South Atlantic about 220 miles from the Argentine coast and at a depth of about 650ft.
The autocrat called for compatriots to avoid "bitterness or revengefulness, which would not make us any better ..."
Mnangagwa's statement said he was aware of the impeachment proceedings and "I will not stand in the way of the people and my party". Constantino Chiwenga, the general who led the takeover, turned the president's pages as he spoke. There's no going back about Mugabe.
The leader of Zimbabwe's war veterans association, an influential voice in national politics, on Friday said Mr. Mugabe must step down at once and urged people to protest against the President.
Mnangagwa said he was aware parliament meant to impeach Mugabe and he supported the move.
Mnangagwa, who fled the country and has not appeared in public during the past week's political turmoil, said Mugabe had invited him to return to Zimbabwe "for a discussion" on recent events. "There is no doubt he will impose a Chinese style of government, which is more favourable towards business, but he will curtail democratic freedoms".
The ruling party was poised to begin impeachment proceedings against Mugabe on Tuesday as Parliament resumed, and it instructed government ministers to boycott a Cabinet meeting Mugabe called for Tuesday morning at State House, the president's official residence.
Last Saturday, Zimbabweans overwhelmingly responded to the call by the war veterans to demonstrate in support of the army's actions.