The 93-year-old Mugabe made his first television appearance since the military intervention.
According to the Anadolu Agency, in a televised speech read in the presence of the country military chiefs, Mugabe acknowledged the concerns raised by the army as well as his own party.
He called for respecting the constitution, "and the need to address differences amicably".
President Mugabe has been asked to step down from presidency and end his nearly four decades of rule, in a latest development in country's ongoing crisis.
The ruling ZANU-PF party has given Monday noon as the deadline or else he would have to face impeachment in Parliament.
Mugabe has already been voted out from the party following a de facto military coup.
The ZANU-PF has replaced Mugabe with recently dismissed Vice President Emmerson Mnangagwa as new party leader.
Mugabe's 52-year-old wife Grace has also been booted out from the party over accusations of "preaching hate, divisiveness and assuming roles and powers not delegated to the office."
The controversial first lady used to be her husband's secretary as well.
Tens of thousands of Zimbabweans attended street protests on Saturday to demonstrate against the Mugabes.
Saturday's marches capped an unprecedented week in which army generals led by General Constantino Chiwenga seized power and placed Mugabe under house arrest. (ANI)