Protesters opposing Egyptian President Mohamed Morsi wave Egyptian flags and a placard reading "Leave", during a protest against him and members of the Muslim Brotherhood at Tahrir square in Cairo. Reuters
An AFP correspondent said at least three people had been killed and many others injured in the clashes, which broke out as thousands of Islamist demonstrators approached the headquarters chanting "traitors" and "Morsi is our president".
The protesters had streamed towards the Guards headquarters on foot from a Muslim Brotherhood rally that drew in tens of thousands at Cairo's Rabaa al-Adawiya mosque.
Shortly before the rallies, around a dozen low-flying military jets screeched across Cairo, a day after they staged a parade leaving a trail of smoke in the shape of a heart in the sky.
It was a show of force that failed to deter Morsi's supporters, however.
The deposed president, who has not been seen since Wednesday, had issued a defiant call for supporters to protect his elected "legitimacy", in a recorded speech aired hours after he was toppled.
The military had said it supported the right to peaceful protest, but warned against violence and acts of civil disobedience such as blocking roads.
Armed forces were also on high alert in the restive Sinai peninsula, bolstering security after Islamist militants killed a soldier during a machinegun and rocket attack.
Clashes also broke out in the Nile Delta province of Sharqiya, hours after chief justice Adly Mansour, 67, was sworn in on Thursday as interim president until new elections.
Mansour called for unity in an interview broadcast on the eve of Friday's rallies.
"All I can say to the Egyptian people is to be one body. We had enough of division," he told Britain's Channel 4 television.
"The Muslim Brotherhood is part of the fabric of Egyptian society. They are one of its parties. They are invited to integrate into this nation and be part of it."
Prominent liberal leader Mohamed ElBaradei defended the military's intervention.
"We asked the army to intervene because the other option was a civil war. We were between a rock and a hard place, and people need to understand that," the former UN nuclear watchdog chief told the BBC.
Ahead of the protests, the army warned Egyptians against resorting to "exceptional and autocratic measures against any political group".
"The armed forces believe that the forgiving nature and manners of the Egyptian people, and the eternal values of Islam, do not allow us to turn to revenge and gloating," added the army, even as security forces rounded up top Muslim Brotherhood officials.
The Islamists accuse the military of conducting a brazen coup against Morsi, Egypt's first democratically elected but divisive president, following massive protests calling for his ouster.
Army chief General Abdel Fattah al-Sisi announced Morsi's overthrow on Wednesday night, citing his inability to end a deepening political crisis, as dozens of armoured personnel carriers streamed onto the streets of the capital.
Military police have since arrested Brotherhood supreme leader Mohammed Badie "for inciting the killing of protesters", a security official told AFP.
Former supreme guide Mahdi Akef was also arrested, state television reported.
Morsi himself was "preventively detained" by the military, a senior officer told AFP hours after his overthrow, suggesting he might face trial.
A judicial source said the prosecution would on Monday begin questioning Brotherhood members, including Morsi, for "insulting the judiciary". Thirty-five of them have been banned from travel.
But controversial public prosecutor Abdel Meguid Mahmud said Friday he was to resign, days after being reinstated, citing possible conflicts of interest in future prosecutions.
Morsi's supporters argue the president was confronted at every turn with a hostile bureaucracy left over by former strongman Hosni Mubarak, overthrown in the country's 2011 uprising.
His rule was marked by a spiralling economic crisis, shortages of fuel and often deadly opposition protests.
US President Barack Obama said he was "deeply concerned" over the developments, but refrained from calling the military intervention a coup.
In May, Washington approved $1.3 billion in military aid to Egypt. That was now under review, said Obama, as he called for a swift return to democratic rule.
The African Union suspended Egypt from the bloc in response to Morsi's ouster, after governments across the Middle East welcomed the military's intervention in varying degrees, with war-hit Syria calling it a "great achievement".