Mohamed Morsi's regime has indicated that it will not give in to the threat of a military coup, just hours after the Egyptian army gave it 48 hours to placate the millions who have taken to the streets calling for the president's departure.

The head of Egypt's armed forces, General Abdel Fattah Sisi, threatened direct military involvement in the political process "if the demands of the people are not realised", in a statement implying that Morsi should either step down or at least call early elections.

The presidency indicated that it viewed the statement as a coup d'etat, and implied that Morsi was safe as long as his administration still had US support.

"Obviously we feel this is a military coup," a presidential aide said. "But the conviction within the presidency is that [the coup] won't be able to move forward without American approval."

The aide's comments implied that the regime was hopeful of continued American support. They also suggested the presidency was banking on the likelihood that the military would not risk upsetting America, which provides it with significant funding.

The US ambassador to Egypt has spent recent days trying to persuade opposition figures to engage in dialogue with Morsi instead of supporting protests.

Renewed military involvement in politics would be welcomed by many Egyptians, who have lost trust in both the presidency and its top-level opposition. Thousands burst towards Tahrir Square in celebration at the news, others set off fireworks. Military helicopters flying overhead were greeted with cheers, and chants of "the army and the people are one hand".

But others were horrified at the prospect of renewed military engagement, and saw it as counter-revolutionary, fearing a repeat of the military junta who ruled for 18 months after the fall of Hosni Mubarak in 2011.