"It is not a military takeover of government," said one general reading a statement.
"We wish to assure the nation that his excellency the president... and his family are safe and sound and their security is guaranteed.
"We are only targeting criminals around him who are committing crimes... As soon as we have accomplished our mission we expect that the situation will return to normalcy."
Armoured vehicles were seen on the streets near the capital Harare on Tuesday as questions mounted over whether Mugabe, who has ruled since independence from Britain in 1980, was still holding onto power.
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Prolonged gunfire erupted near Mugabe's private residence in the suburb of Borrowdale early Wednesday, a witness told AFP. No further details were available.
The shooting came after Mugabe's ZANU-PF party on Tuesday accused army chief General Constantino Chiwenga of "treasonable conduct".
The public dispute has presented a major test for Mugabe, who is in increasingly frail health.
Chiwenga had demanded that Mugabe stop purges of senior party figures, including vice president Emmerson Mnangagwa, who was dismissed last week.