"We need an immediate meeting between the president, defence and interior ministers, the ruling party, the Salafis and the National Salvation Front to take urgent steps to halt the violence and start serious dialogue," the former IAEA chief, ElBaradei, wrote on his Twitter account.
Two more protesters were shot dead today in Cairo's iconic Tahrir Square on the seventh day of what has become the deadliest wave of unrest since Mursi took power in June.
ElBaradei's proposal for meeting comes two days after the main opposition bloc, the National Salvation Front led by him, rejected a call made by Islamist Brotherhood leader Mursi to hold a "national dialogue".
The Front, a grouping of mostly liberal and leftist politicians, on Monday demanded Mursi to take responsibility for days of fatal violence in the country, suspend the newly approved constitution and sack a public prosecutor he appointed last November.
The worst violence hit the Suez Canal city of Port Said, where rage was fuelled by death sentences passed against soccer fans for deadly riots last year. Mursi responded by announcing on Sunday a month-long state of emergency and curfew in Port Said and two other Suez Canal cities.
Egypt's army chief Gen Abdel Fattah al-Sissi, who is also the country's Defence Minister, yesterday warned that the current wave of unrest that triggered political crisis in the country "could lead to a collapse of the state", even as the death toll mounted to 60 in days of protests and violence.
"The continuing conflict between political forces and their differences concerning the management of the country could lead to a collapse of the state and threaten future generations," Sissi said.
A total of 590 people were injured in violence across the country yesterday alone, with most of them in Port Said.
Meanwhile, President Mursi left for Germany to hold talks with Chancellor Angela Merkel. Morsi, who was expected to stay in Berlin for two days, has cut short his European tour to just a few hours. He also cancelled his trip to Paris.