In scenes reminiscent of Zimbabwe's independence in 1980, crowds packed the cities, waving flags and chanting for Mugabe to resign.
The war veterans claimed that Mugabe swapped speeches to avoid resigning during the address to the nation.
His sacking from the party capped a dramatic week after the military seized power on Wednesday saying it wanted to remove "criminal elements" around the president.
The takeover was preceded by Mugabe dismissing Vice President Emmerson Mnangagwa.
Mugabe astonished Zimbabweans with his defiance in a national address Sunday night after being fired as party leader.
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The opposition leader says the upheaval could undermine the opportunity for a "fresh start" after moves by the military and others against Mugabe.
ZANU-PF's action follows a weekend of high drama in Harare that culminated in reports Mugabe had agreed to stand down - only for him to dash the hopes of millions of his countrymen in a freakish and rambling national address on Sunday night.
"It's absolutely astounding. Mugabe behaves as if nothing ZANU-PF said (Sunday) was of any relevance", he told AFP.
Mugabe's wife Grace, 52, secured prime position to succeed him, sidelining the vice president, Emmerson Mnangagwa, who was sacked.
A notice by Mr Mugabe's chief secretary announced Tuesday morning's Cabinet meeting at State House and said all ministers "should attend".
"He might not leave tomorrow or next week, but he is clearly at the end of his political life", said Mr Eldred Masunungure, a politics lecturer at the University of Zimbabwe.
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With the generals responsible seated next to him, Mugabe gave a lengthy speech acknowledging some problems with the economy and the Zanu-PF party - from which he was ousted earlier in the day - but made no mention of leaving office.
The party was yet to comment on its next steps after that deadline passed.
Chris Mutsvangwa, head of the influential war veterans' association, called for protests and demanded that Mugabe be impeached.
However, Mugabe did not offer any concessions in a televised speech Sunday. We will stage a sit in until Mugabe is gone.
He also says the war veterans' association is going to court to argue that Mugabe is "derelict of his executive duty".
But now, with Mugabe refusing to resign despite repeated attempts at persuasion, and with parliament threatening to begin impeachment proceedings Tuesday, the military could be on a long and complicated path with a formidable opponent: Mugabe himself.
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As a outcome, the call by the MDC and its alliance partners for an all-inclusive process to take the country to legitimacy is the only way forward.