A 10-year-old boy has been shot dead while walking near the site of clashes between supporters and opponents of deposed president Mohamed Morsi in Egypt's northern city of Suez, security and medical sources said.

In Cairo, a 21-year-old man died after being shot in the chest during clashes between the two camps, and across the country another 14 people were injured in confrontations, the head of the ambulance authority told the state newspaper al-Ahram.

Morsi's supporters have staged frequent protests in towns and cities, many of them after Friday prayers, since the army deposed him on July 3 in response to mass protests against his rule, and arrested most of the top leaders of his Muslim Brotherhood group.

At least 35 people have been arrested during the latest protests across the country on Friday.

The marches in multiple districts of Cairo and other cities were commemorating the August 14 storming by security forces on two pro-Morsi protest camps in the capital that killed hundreds of Islamists.

In one of the marches, protesters attempted to enter Rabaa al-Adawiya Square, which was the site of the biggest sit-in camp, in an eastern neighbourhood of Cairo. Security forces, who had sealed off the square with barbed wire and armoured vehicles, drove the protesters off with volleys of tear gas.

In Suez, around 500 supporters of Morsi gathered in the central Awel-el-soor neighbourhood and chanted slogans against the army and police.

Clashes broke out with opponents of Morsi and rocks were thrown and gunfire exchanged, witnesses said.

The child, named Samir El-Gamal, was hit by a bullet in the back of the head, the sources said, while he was walking with his mother near the site of the clashes. His mother was unharmed, but the boy died on the spot, they said.

Trading blame

Muslim Brotherhood members accused the security forces of using live rounds to disperse their protest, residents of Suez said.

Police said the bullets had come from the opponents of the protesters, not from security forces.

The child's family accused the Brotherhood of responsibility for their child's death, the state news agency MENA said.

The interim government installed in July has waged a broad crackdown on the Brotherhood, accusing its leaders of fomenting violence or terrorism, accusations they deny.

The government has promised a return to democratic rule next year, under a new constitution. In the interim, the political turmoil that has gripped Egypt since the overthrow of Hosni Mubarak in early 2011 continues to undermine stability.

Elsewhere, hundreds of pro-Brotherhood protesters tried to force their way into the embassy of the United Arab Emirates in Cairo and attacked its guards, but police used teargas to disperse them, the state newspaper al-Ahram said.

Since Morsi was deposed, the UAE and other Gulf Arab allies have shown strong support to the interim government, pledging billions of dollars to help shore up Egypt's fragile finances.