Morsi's supporters said more than 100 people were killed and accused security forces of opening fire on unarmed protesters.
The Health Ministry says 38 people were killed.
VOA's Cairo bureau chief, Elizabeth Arrot, told RFE/RL that it is unclear what provoked the violence.
"Last night, it was very tense before these rallies got under way, and then certainly it's what many people said that they thought it would be, 'a predawn raid of some sort.' It is contested whether or not the army moved first or they were responding to provocations," she says. "Both sides say that the other acted first."
The bloodshed is expected to deepen the turmoil in Egypt following Morsi's removal by the army on July 3.
Egypt's interior minister denied police had fired on protesters and said a nearly monthlong sit-in in Cairo demanding Morsi's reinstatement be brought to an end "soon in a legal manner."
He also said Morsi was likely to be transferred to the same Cairo prison where former President Hosni Mubarak is now held.
Morsi has been held at an undisclosed location since July 3.
Meanwhile, reports that Morsi is under investigation in connection with the prison break killings of guards and soldiers during Egypt's 2011 uprising has signaled an escalation of the military’s confrontation with Islamists.
The military had urged Egyptians to join rallies on July 26 in support of its fight against what it calls "violence and terrorism." Hundreds of thousands heeded the call.
The Muslim Brotherhood responded by calling on its supporters to join protests against the ouster of the Islamist president by Egypt's army.
Tensions were high in Cairo early on July 27 with thousands of Morsi supporters hunkered down around a mosque, while an enormous crowd supporting Morsi's ouster remained at Tahrir Square.
A Morsi opponent in Tahrir Square said people did not want the Islamist leadership.
"I have come out to support all of the martyrs and because we don't want the Muslim Brotherhood or terrorism in this country," the man said. "We want the people to be united -- Muslims and Christians united."
But a supporter of the deposed president blamed the tensions on army chief Abdel Fattah al-Sisi, who had called for the July 26 demonstrations in a bid to claim a popular mandate for Morsi's ouster.
"The view of the people has changed after the speech [by Egyptian interim Defense Minister General Abdel Fattah al-Sisi]," the man said. "It had threatening language in it. Al-Sisi asked for a mandate from the other side, meaning, 'I want a mandate from half of the people to kill the other half.' So this is nonsense. And it's clear that it's aimed at those outside of Egypt more than at those within."
It was an Egyptian court that ordered the ousted president to be held in detention for 15 days while investigators probe allegations he colluded with the Palestinian group Hamas to storm police stations and prisons during the 2011 uprising.
Morsi and several other jailed Muslim Brotherhood leaders were freed in the 2011 prison breaks.
The Muslim Brotherhood said the court order resembled the tactics used by the regime of Hosni Mubarak, Egypt's longtime authoritarian ruler who was toppled in 2011.
Hamas, an offshoot of the Muslim Brotherhood which rules the Gaza Strip, denounced the court order.
Rupert Colville, spokesman for the UN High Commissioner for Human Rights, said Morsi should either be released or face "clear and transparent" charges.
"Our position on Mr. Morsi and the secretary-general's position is very clear that he should either be released -- not just him but also the other Muslim Brotherhood leaders who have been detained -- or, if they are being formally charged with something, that needs to be made very clear and very transparent, according to the law," Colville said.
Some 200 people have been killed in violence in Egypt during the three weeks since Morsi was ousted by the military.