The moves came a day after at least 200,000 protesters filled Cairo's central Tahrir Square to denounce the decrees Morsi issued last week, which place him above oversight of any kind, including by the courts.
Threatening to turn the dispute into violent street clashes, Morsi's Muslim Brotherhood and the more radical Islamist Salafi Al-Nour party, called for a counter-demonstration this weekend in Tahrir Square, where Morsi's opponents have been holding a sit-in for over a week.
Morsi says the decrees are necessary to protect the "revolution" that helped drive Hosni Mubarak from office last year as well as the nation's transition to democratic rule. The constitutional declaration also provides the 100-member panel drafting a new constitution with immunity from the courts.
In a sign the dispute may take a sharp turn, the Supreme Constitutional Court said in a statement that it will go ahead with plans to rule Sunday on whether to dissolve the assembly writing the new constitution, which is dominated by the Brotherhood and its Islamist allies.
"The court is determined to rise above its pain and continue its sacred mission until the end, wherever that takes us," Maher Sami, the high court's deputy chairman, said in a televised speech.
The expected decision on Sunday, regardless of which way it goes, would constitute a direct challenge to Morsi, who took office in June as Egypt's first freely elected president but has enraged pro-democracy activists who claim he is acting too much like the authoritarian leader he replaced.
Complicating matters, the constitutional panel was rushing to wrap up its work and some members said a final draft could be completed as early as Thursday. This would allow the president to call for a nationwide referendum on the document even before the court convenes Sunday, circumventing its decision.
In an unprecedented move, meanwhile, Egypt's highest appeal courts went on strike to protest the presidential decree. Judges with the high and lower courts of appeal said they would not return to work until Morsi rescinds his decrees, according to state TV. Many of the country's courts already had stopped functioning due to individual strikes.
The high court of appeal is led by Mohammed Mumtaz Metwali, who also chairs the Supreme Judiciary Council, which oversees the nation's court system. Members of the council met Morsi on Monday to discuss his decrees.
In a statement, judges of the high appeals court, known as the Court of Cassation, denounced Morsi's decrees as an "unprecedented" assault on the judiciary and its principles. It said the decision to halt work at all its circuits was justified by the "magnitude" of the crisis.
"This is the highest form of protest," said Nasser Amin, the head of the Arab Center for the Independence of the Judiciary and the Legal Profession.
Morsi and his allies in the Muslim Brotherhood have accused the judiciary of being dominated by Mubarak-era appointees who are trying to undermine the new leader, allegations the judges have rejected.
The constitutional court ruled in June to dissolve parliament's lower chamber, which is dominated by Islamists, on grounds that the law governing the elections didn't provide equal opportunities for candidates. There were warnings before the vote that such legal pitfalls might be forthcoming but the elections went ahead anyway.
The court denounced Morsi's claim that it was part of a "conspiracy" against him.
"The allegation that the (June) ruling was reached in complicity with others to bring down elected state institutions and consequently the state's collapse ... is incorrect and untrue," said Sami, the high court's deputy chairman.
In response to Tuesday's massive anti-Morsi protests, the Brotherhood and other Islamist parties announced plans to hold a rival rally on Saturday in Tahrir Square, dubbed "In support of legitimacy and Shariah (Islamic law)."
Previous rallies where Islamists and secular forces met in the square have turned violent.
The liberal opposition has said it will not enter a dialogue with the president about the country's latest political crisis until Morsi rescinds his decrees. Activists planned another massive rally on Friday.