Both the ruling party's youth wing and the main opposition party called for civilian rule to be protected, while analysts called the crisis a potential turning point.
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Army chief General Constantino Chiwenga on Monday warned Mugabe to "stop" purges of the ruling ZANU-PF party after the president abruptly sacked vice president Emmerson Mnangagwa last week.
Mnangagwa had clashed repeatedly with First Lady Grace Mugabe who is widely seen as vying to replace the 93-year-old leader when he dies.
"We must remind those behind the current treacherous shenanigans that when it comes to matters of protecting our revolution, the military will not hesitate to step in," Chiwenga told top brass at Harare's King George VI military headquarters in an unprecedented intervention.
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He appeared to be referring to the increasingly open efforts of Grace Mugabe to elevate her public position and publicly undermine her opponents -- including Mnangagwa.
The main opposition Movement for Democratic Change (MDC) called for civilian rule to be defended following Chiwenga's threat.
"No one wants to see a coup -- not that I am saying there is going to be a coup. If the army takes over that will be undesirable. It will bring democracy to a halt, and that is not healthy for a nation," the MDC's shadow defence minister, Gift Chimanikire, told AFP.
ZANU-PF's Youth League, which strongly supports Grace Mugabe, said in a statement that Chiwenga would not be allowed to pick Zimbabwe's leaders.
"We will stand guard in defence of the revolution -- like the people of Turkey last year who repelled rogue security forces from interfering with an elected government," it said.
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Neither the ZBC state broadcaster nor the government-run Herald daily covered the army chief's open threat to Mugabe, prompting senior commanders to demand why his intervention went unreported.
Speculation has been rife in Harare that Mugabe could now remove Chiwenga who is seen as an ally of ousted Mnangagwa.
The crisis "marks another landmark ominous moment in the ongoing race to succeed" Mugabe, said political analyst Alex Magaisa in an online article.
'A turning point'
"(Mugabe) has previously warned the military to stay away from ZANU-PF's succession race.
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"His authority over the military has never been tested in this way. If he does nothing, it might be regarded as a sign of weakness. If he puts his foot down, it could result in open confrontation."
Chiwenga, 61, was on official business in China when Mnangagwa was removed. They were both prominent figures in the struggle for independence from Britain, along with Mugabe.
Mnangagwa was widely seen as Mugabe's most loyal lieutenant having worked alongside him for more than 40 years and his ouster sent shockwaves through the region.
He fled the country and is thought to be in South Africa but has yet to make a public appearance following his searing five-page condemnation of Grace's ambition and Mugabe's leadership style.
Shadrack Gutto, the director of the Centre for African Renaissance Studies at the University of South Africa, told AFP that if Grace attempted to take control, the army "will throw her out and she can go into exile or die".
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"They will not accept Grace Mugabe as president of Zimbabwe... (This) is a turning point in Zimbabwe because Robert Mugabe is semi-senile."
Wright Chirombe, a 36-year-old barber in Harare, welcomed the army's pledge to intervene.
"We have a ruling party that has been hijacked by individuals who want to create a dynasty. All these people want is their own gains and to protect those gains. No one cares about the ordinary people's suffering," he said.
But Zimbabwe's business community, which is already contending with shortages of foreign currency and essential supplies caused by economic uncertainty, was more cautious about Chiwenga's intervention.
"The general can talk about the revolution but it does not help the ordinary people. The people just want bread and butter," said 37-year-old Oscar Muponda who runs a technology retailer in the capital.
