Several have died in clashes near a Cairo university that broke out soon after the interim president appealed for calm. Meanwhile, the family of ousted President Morsi has threatened legal action if he is not released.
The death toll in Egypt rose on Tuesday as Health Ministry officials confirmed six fatalities from clashes that had taken place close to Cairo's main university overnight.
Fighting had broken out between supporters of deposed President Mohammed Morsi who were staging a sit-in nearby, and opponents of the ousted leader.
Al-Ahram newspaper reported that six had died, citing a health official speaking on the conditition of anonymity. The Muslim Brotherhood's Freedom and Justice Party also confirmed the reports of new deaths.
"Leaders of the military coup continue to terrorize the peaceful protesters in Egypt," the Muslim Brotherhood claimed on its website Tuesday.
The latest violence came on the anniversary of Egypt's 1952 revolution, which overthrew the country's 150-year-old monarchy, and just hours after interim President Adly Mansour had used the occasion to appeal for calm and reconciliation.
"We want to open a new page in the book of the history of the nation without rancor, hatred or confrontation," Mansour said Monday night. "It's high time to build a country that has reconciled with the past in order to build the future."
Tensions have worsened on the street between those calling for Morsi's return to power as Egypt's elected president and those who support the the formation of a new government. Violence sparked by the unrest has claimed over 100 lives since the military removed Morsi from power in early July.
The Muslim Brotherhood has rejected the authority of interim government, led by President Mansour, Prime Minister Hazem el-Beblawi and a 35-member Cabinet.
Family wants to see Morsi
Morsi's disappearance has contributed to the turmoil gripping Egypt. The military has neither disclosed his location, nor allowed him to show any sign of life to the outside world in almost three weeks.
The deposed leader's family has threatened to seek international justice if Morsi continues to be held in isolation and without charge.
"We accuse [Egyptian army chief Abdel Fattah] al-Sissi and the group that supported the coup of kidnapping the citizen and president, Mohammed Morsi," his son Osama told a Monday press conference in the capital city.
"We are taking local and international legal measures against Abdel Fattah al-Sissi, the leader of the bloody miltiary coup, and his putschist group," Morsi's daughter, Shaimaa Mohamed Morsi, said.
The military maintains that it has chosen to withhold information on the ex-president's whereabouts as a safety measure.
On July 3, the military seized control of the government in direct response to mass demonstrations calling for Morsi's removal. The opposition - driven by a group called Tamarod that accumulated millions of signatures, according to its own account - had demanded new elections because Morsi had failed to uphold the goals of the revolution that toppled Hosni Mubarak in 2011.
kms/tj (AP, AFP, Reuters, dpa)