Emmerson Mnangagwa said he fled abroad two weeks ago when he learned of a plot to kill him, and he would not return until he was sure of his security.
The ruling Zanu-PF party is expected to begin impeachment proceedings in parliament later on Tuesday.
Mr Mugabe is accused of allowing his wife to “usurp constitutional power”.
Speaking from an undisclosed location on Tuesday, Mr Mnangagwa said the 93-year-old president should heed the “clarion call” of his people and step down.
“I told the President that I would not return home now until I am satisfied of my personal security, because of the manner and treatment given to me upon being fired,” he said in a statement.
Mr Mnangagwa’s dismissal earlier this month was seen by many as clearing the way for Mr Mugabe’s wife Grace wife to succeed him as leader.
The move riled top army officials, who stepped in and put Mr Mugabe under house arrest, though he nominally remains the president.
Emmerson Mnangawa more or less accused President Mugabe of trying to have him killed. The statement from the former vice-president gave an extraordinary insight into the vicious power struggles that preceded last week’s military intervention here.
Mr Mnangagwa said his security guards had warned him of plans to “eliminate” him, after he was sacked earlier this month. He promptly fled to South Africa.
On Monday night Zimbabwe’s army generals claimed that Mr Mnangagwa had agreed to return home as part of a transitional roadmap.
That roadmap now sounds like wishful thinking, as parliament here prepares to impeach the president, and Mr Mnangawa angrily demands that his former boss respects the will of the people or faces humiliation.
Impeachment proceedings are set to go ahead after a deadline set by the party for Mr Mugabe to stand down came and went.
Speaking outside a party meeting on Monday, member of parliament Paul Mangwana said of the president: “He is a stubborn man, he can hear the voices of the people, but is refusing to listen.”
Impeachment in Zimbabwe can only occur in specific scenarios, on grounds of “serious misconduct”, “violation” of the constitution or “failure to obey, uphold or defend” it, or “incapacity”.
“The main charge is that he has allowed his wife to usurp constitutional power when she has no right to run government,” Mr Mangwana said.
“He has refused to implement the constitution of Zimbabwe – particularly we had elections for the provincial councils, but up to now they have not been put into office.”