CAIRO (AFP) - Opponents of deposed president Mohamed Mursi flocked to Tahrir Square on Sunday as his supporters massed for rival demonstrations to keep up the pressure on the army for toppling him.

The rallies will raise the stakes as a coalition that backed Mr Mursi's ouster wavered over the choice of Nobel Prize laureate Mohamed ElBaradei as interim prime minister to lead the country out of the bloody crisis.

They come two days after demonstrations by tens of thousands of members of Mr Mursi's Muslim Brotherhood degenerated into violence that killed 37 people and injured 1,400 across the country.

The Tamarod movement, which engineered mass protests that culminated in the military's overthrow of Mr Mursi on Wednesday, led calls for people to gather at Tahrir and Ittihadiya presidential palace to "complete the revolution".

The Brotherhood's Freedom and Justice Party (FJP) called on Mursi supporters to converge on Rabaa al-Adawiya mosque, Cairo University and the Republican Guard headquarters.

The demonstrations, the FJP said, were to support the "legitimacy" of Mr Mursi's election in June last year and to "reject the military coup" that ousted him.

Mr Mursi's single year of turbulent rule was marked by accusations he failed the 2011 revolution that ousted autocratic former president Hosni Mubarak by concentrating power in Islamist hands and letting the economy nosedive.

In an interview published on Sunday, Mr ElBaradei called for "inclusion of the Brotherhood in the democratisation process".

"No one should be taken to court without a convincing reason. Former president Mursi must be treated with dignity," the winner of the 2005 Nobel Peace Prize told German news weekly Der Spiegel.

The official Mena news agency said on Saturday that caretaker President Adli Mansour had appointed Mr ElBaradei, only for his office to later deny any final decision had been taken.

Salafi Islamists, who gave their backing to Mr Mursi's ouster in a military coup on Wednesday, were holding out against Mr ElBaradei's appointment, officials close to the talks told Agence France-Presse.

Presidential adviser Ahmed al-Muslimani said Mr ElBaradei, the former head of the United Nations nuclear watchdog, remained the "strongest candidate".

"He is on top of the list of names," Mr Muslimani told AFP.

But by Sunday morning, after another round of talks, a senior Salafi politician said his Al-Nour party would not accept Mr ElBaradei.

"Our position is simple. There are two reasons to reject ElBaradei: we need a technocratic economic figure; and we need to end polarisation on the street," said Mr Nader Bakkar.

"We can't talk of national reconciliation and then make Mursi's most ardent opponent prime minister."

An official close to Mr ElBaradei conceded there were fears of alienating Al-Nour, which won almost a quarter of votes in a 2011 parliamentary election, and "driving them" into Mr Mursi's camp.

Mr Mursi, who has been in custody since overnight on Wednesday, had issued a defiant call for his supporters to defend his "legitimacy" as Egypt's first freely elected president, in a recorded speech released shortly after his ouster.

Friday's violence erupted despite talk of peaceful protests, with Cairo and the Mediterranean city of Alexandria the hardest hit.

The bloodletting continued, with gunmen on Saturday killing a Coptic Christian priest in the Sinai Peninsula and militants on Sunday blowing up a gas pipeline to Jordan as Islamists fired on the security forces.

Russia's President Vladimir Putin warned the stand-off threatened to degenerate into a civil war.

"Syria is already in the grips of a civil war, unfortunately enough, and Egypt is moving in that direction," news agencies quoted Mr Putin as saying.

"We would like to see the Egyptian people avoid this fate."

Moscow has previously called on all sides in the crisis to exercise "restraint".

United States President Barack Obama insisted overnight that the US was "not aligned" with any political party or group in Egypt following Mr Mursi's ouster.

"The future path of Egypt can only be determined by the Egyptian people," the White House quoted him as saying.

And former British prime minister Tony Blair said the army had no choice but to overthrow Mr Mursi, in a column published in the Observer newspaper.

"The events that led to the Egyptian army's removal of President Mohamed Mursi confronted the military with a simple choice: intervention or chaos," Mr Blair wrote of the mass protests calling for Mr Mursi's ouster.