The National Salvation Front, a recently created umbrella group comprised of liberal and leftist groups, issued a statement in which it said that the "authority" had lost its legitimacy and called for mass protests on Friday.
The statement follows deadly clashes between supporters of Morsi and opposition protesters on Wednesday that left six dead and almost 700 injured. The clashes erupted after supporters of the president dispersed a sit-in by non-Islamist groups following a mass protest on Tuesday.
Hundreds of thousands marched to the presidential palace in Tuesday's demonstration to protest against recent decisions by Morsi they deemed "dictatorial."
"The people have noticed an evident abandonment of the duty to protect individuals and assets by the authorities which lost them their legitimacy," the statement read.
The clashes broke out after two weeks of simmering tension due to a 22 November constitutional declaration by Morsi, which gave him immunity from judicial oversight and protected the Constituent Assembly – which drafted a controversial constitution – from dissolution.
The opposition argues that the draft constitution – which will be put before a popular referendum next week after having been written by Egypt's Islamist-led Constituent Assembly – would have an adverse effect revolutionary demands including civil liberties and social benefits.
"We had hoped the president would have responded to repeated demands to annul the constitutional declaration and postpone the constitutional referendum until a national consensus on the draft constitution was reached," it stated.
The front also rejected invitations to hold dialogue after Wednesday's events, which it had accused the Muslim Brotherhood of inciting in a previous statement.
"Following the latest violent events, it is difficult for the front to negotiate, ignoring the innocent blood spilt," it asserted, saying that the presidency and the government had failed to take the necessary steps and decisions to prevent the bloodshed.
"The president is ignoring the attempts of the front to save the nation and his ignoring the demands of the people and their protests has closed the door for any efforts for dialogue," the group added.
Members of the front include the Constitution Party, co-founded by opposition leader Mohamed El-Baradei, the Egyptian Popular Current, the 6 April Youth Movement, the Egyptian Social Democratic Party, the Socialist Popular Alliance Party, the Kifaya movement and others.
The front insisted on its original demands of scrapping the constitutional declaration and suspending the constitutional poll.
Thousands of anti-Morsi protesters reached the presidential palace on Thursday to condemn what they said were attacks by the Brotherhood and other Morsi supporters on the opposition.
"Down with the rule of the Supreme Guide," "Down with Morsi" and other chants rang out as thousands of protesters walked towards Al-Khalifa Al-Maamoun, which intersects Marghany Street overlooking the palace.
Streets adjacent to the palace were barricaded and manned with Presidential Guard officers and soldiers. The guard ordered protesters to leave the area by 3pm Cairo local time and imposed a curfew on the area until further notice.
In several governorates, the Muslim Brotherhood's offices were attacked on Thursday by unknown assailants for the second day in a row. The attacks included the Brotherhood's main headquarters in Cairo's Moqattam district, which was ransacked, and another in the upscale district of Maadi.
The Brotherhood had issued its own statement saying Morsi supporters at the palace were attacked by paid thugs and vowed to continue their fight until realising the goals of the revolution.
Morsi supporters claim the withdrawals that have plagued the Constituent Assembly were a form of political pressure by liberal forces. Many of the president's supporters see the 22 November constitutional declaration as a legitimate move by a president who was elected by the people in Egypt's first free presidential polls.