Robert Mugabe is facing impeachment this week if he doesn't resign following a rambling television address on Sunday night in which the Zimbabwean President refused to quit. 

Now the ruling Zanu-PF party say he has until noon (1000 GMT) on Monday to stand down or they will begin impeachment proceedings after the 93-year-old leader defied expectations that he would resign.

Mugabe stunned Zimbabweans in his Sunday night address by avoiding any mention of resignation, pledging instead to preside over a congress next month of Zanu-PF, which had sacked him as its leader only hours earlier.

Parliament does not sit on Mondays so any impeachment would have to wait until Tuesday, although a vote may not necessarily take place the same day.

Moments after Mugabe's address, the leader of Zimbabwe's liberation war veterans, who have been among the most vocal in calling for Mugabe's resignation, Chris Mutsvangwa, told Reuters they would lead public protests in the streets of Harare, cranking up the pressure on Zimbabwe's ruler of the last 37 years.

Having been sacked by his party, Mugabe has run out of options but appears to be steadfastly clinging to the very last vestiges of power.

In a confusing speech on Sunday night the 'grand-old man' of African politics defied expectations by refusing to resign.

There was even speculation that he read the wrong speech in his live television address, or skipped over passages about standing down.

But he said the military had done nothing wrong by seizing power. 

'Whatever the pros and cons of how they [the army] went about their operation, I, as commander-in-chief, do acknowledge their concerns,' he said, referring to the army's move last week to take over the state broadcaster in the capital Harare.

He also said 'the [Zanu-PF] party congress is due in a few weeks and I will preside over its processes'.

Anxious Zimbabweans have been trying to decipher a barely audible aside comment he made to military chief Constantino Chiwenga at the end of the address. In the audio, which is not clear, Mugabe refers to a 'long speech' or a 'wrong speech'.

Zanu-PF's central committee had earlier named Emmerson Mnangagwa as its new leader. It was Mugabe's sacking of Mnangagwa as his vice-president — paving the way for his wife Grace to succeed him — that triggered the army to seize control on Wednesday.

On Saturday, hundreds of thousands took to the streets of the capital Harare to celebrate Mugabe's expected downfall and hail a new era for their country.

The huge crowds in Harare have given a quasi-democratic veneer to the army's intervention, backing its assertion that it was merely effecting a constitutional transfer of power, rather than a plain coup, which would risk a diplomatic backlash.

But some of Mugabe's opponents are uneasy about the prominent role played by the military, and fear Zimbabwe might be swapping one army-backed autocrat for another, rather than allowing the people to choose their next leader.

Armoured vehicles manned by soldiers were still stationed on some street corners in the capital on Monday.

Additional reporting from Reuters.