Officials close to the talks between Mugabe and the military had said Mugabe was resigning.
The army commander who put Mugabe under house arrest just days ago helped Mugabe to turn the pages of his speech as he addressed the nation.
Zimbabweans accustomed to hours-long speeches by Mugabe had been wondering how long this one would take.
The state-run broadcaster introduced Mugabe's speech by saying: "Sit back, relax and join us."
Ruling party leaders have told Mugabe to step aside by noon Monday (11pm NZ time) or face impeachment.
He says people cannot "ride roughshod over party rules and procedures".
Mugabe shook the hands of the military leaders who put him under house arrest just days ago during the broadcast.
He says he is aware of a "whole range of concerns," including the economy, which is going through "a difficult patch".
Mugabe is the world's oldest head of state.
He says "the pillars of state remained functional" amid the crisis, in which Zimbabweans rallied by the tens of thousands against him and ruling party leaders told him to step aside or face impeachment.
The MailOnline had earlier reported Mugabe had agreed to step down after 37 years as leader.
Mugabe broke down in tears and asked for his dead wife and son before meeting army chiefs on Sunday after being ousted as leader of Zimbabwe's Zanu-PF party, one of his aides told MailOnline.
The frail 93-year-old has until noon local time on Monday to resign as president or impeachment proceedings will start, Zanu-PF said.
Mugabe was replaced by the vice president he previously sacked, Emmerson 'Crocodile' Mnangagwa, after all 10 Zimbabwean provinces passed no-confidence motions against the dictator two days earlier.
Ahead of his meeting with army officials to discuss his exit, Mugabe was "wailing profusely" and saying that he wished he could speak to his dead wife, Sally Mugabe, and his late son, Michael Nhamodzenyika, who died from cerebral malaria in 1966 at the age of three.
"He spends most of his time looking at an old photograph of Sally. It is terrible," the aide said of Mugabe's first wife, who died of kidney failure in 1992.
In 1996, Mugabe went on to marry his current wife, "Gucci" Grace, who was also expelled from her role as head of the Zanu-PF Women's League "forever".
The frail dictator has been staging a hunger strike over his confinement in house arrest and is refusing to take regular baths or speak, the aide added.
The only person who has managed to get through to him was the Catholic cleric Father Fidelis Mukonori, who is mediating between Mugabe and the generals, the aide added.
Images of the meeting showed Mugabe, who wore a black suit, white shirt and red tie, with his hand to his head and deep in conversation with senior security officials, including army chief Constantino Chiwenga who led the military takeover earlier this week.
"President Robert Mugabe this afternoon met with Zimbabwe Defence Forces Generals at State House," the Herald said on its Twitter feed, accompanied by photographs.
Mnangagwa is within touching distance of the presidency, delayed only by Mr Mugabe's continued refusal to step down.
Following his resignation, Mugabe could live as an "elder statesman" in Zimbabwe, or travel to a country where he has property, including South Africa, Dubai or Singapore.
While Mugabe has been removed from his role of Zanu-PF party leader, his title as Zimbabwean president remains.
Impeaching the president was to be the next step when Parliament resumes Tuesday, and lawmakers would have "definitely" put the process in motion, the main opposition's parliamentary chief whip told The Associated Press.
- Additional reporting: Daily Mail, AP
