The warnings came as at least 40 people were killed in a shooting incident in Cairo, outside the headquarters of the Republican Guard - the largest single death toll since protests forced the president from power.
According to a statement from an army spokesmen aired on Egyptian TV, "a terrorist group" attempted to occupy the building to free the ex-President, killing an army officer. The Muslim Brotherhood accused the security forces of attacking protesters there.
Dozens have been killed and more than 1,000 wounded in clashes since the president's exit last week. Both pro and anti-Morsi activists are on the streets of Egypt's cities.
In Cairo, supporters of the ex-president have been gathered at the Rabaa al-Adawiya mosque in Cairo, with thousands marching from the mosque on Sunday to the barracks of the Presidential Guard, where they believe Morsi is being held. His detractors gather in Tahrir Square.
A medic from the area, Hesham Agami, told AP ambulances were unable to transport more than 200 wounded to hospitals because the military had blocked off the roads.
The escalating chaos has alarmed Western leaders and other allies. "Syria is already in the grips of the civil war ... and Egypt is moving in the same direction," Putin told Russian state news agency RIA Novosti during a visit to Kazakhstan's capital Astana.
Pro-reform leader Mohamed ElBaradei condemned the violence and also called for an investigation.
Violence begets violence and should be strongly condemned. Independent Investigation a must. Peaceful transition is only way .— Mohamed ElBaradei (@ElBaradei) July 8, 2013
Ahmed el-Hawary, founding member of the al-Dustour Party and member of June 30 front, told Al Jazeera the killings were "catastrophic".
"We cannot blame the Muslim Brotherhood without blaming the army; they're both held accountable for this catastrophe. The Brotherhood needs to stop placing its supporters on the frontline, and the army must be more self-controled," he said.
"June 30 was all about avoiding a civil war and the spilling of blood. This doesn't mean, however, targeting a specific sect."
Demanding that the army broadcasts all video recordings taken by surveillance cameras in the sight of clashes, he accused the Brotherhood of trying to "play victims to gain international sympathy, yet losing whatever is left of the sympathy at home."
"A speedy formation of the new cabinet is essential at this point, and although consensus is critical, Egypt must not be the hostage of a concurrence based on non-pertinent arguments," he said, referring to the Nour party's opposition to proposed prime minister candidates.
Ahmed Aref, the senior Brotherhood spokesman, told The Daily Telegraph: "We will continue our peaceful demonstrations. We are the owners of a just cause. Legitimate rights do not disappear with time. We are facing an enforced disappearance of the legitimate president."
Armed Islamist group Salafi Jihad called for an "intifada", a "clarion call for Islamic revolution" in the wake of the killings.
"Anyone who knows an advocate or a sheikh or a revolutionary should call him to urge him to mobilise," a statement said.
On Saturday, gunmen killed a Coptic Christian priest, Father Mina Aboud Sharween and Muslim Brotherhood leaders have decried Christians for joining anti-Morsi protests.
Morsi was replaced on Thursday by Adly Mansour - the head of the Supreme Constitutional Court - who promised to hold elections soon. No firm date has been given.