Ten people were killed in three separate attacks in Egypt on Monday, most of them soldiers and police officers, in a fresh round of violence that followed violent clashes across the country one day earlier.

The deadliest attack was in the Suez Canal city of Ismailia, east of Cairo, where masked gunmen opened fire on an army patrol. Six soldiers were killed, including a lieutenant.

Meanwhile on Sinai, a suicide car bomber attacked the security headquarters in the southern city of El-Tor. Four people were killed, including the bomber, and 55 more were injured.

Mohamed Ibrahim, the interior minister, confirmed that the attack was a suicide bombing and said it was meant to "distract" people and cause instability.

Near-daily attacks on the peninsula have escalated in the three months since the Egyptian army ousted President Mohamed Morsi. But this was among the first in South Sinai, a popular tourist destination which has been mostly quiet for years.

Attackers also targeted the compound housing Egypt's main satellite earth station in Maadi, a suburb south of Cairo, firing at least two rocket-propelled grenades.

The dawn attack caused only minor damage, but was nonetheless the most significant attack in the capital since a failed assassination attempt against the interior minister last month.

"We are expecting worse," a senior security official told the Associated Press.

Fresh protests called

Monday's violence comes a day after at least 51 people were killed in clashes between security forces and armed civilians, on one side, and Morsi's supporters on the other.

Thousands of Egyptians took to the streets on Sunday to celebrate the October 6 holiday, which marks the beginning of Egypt's 1973 war against Israel. Morsi's supporters organised their own counter-protest, hoping they could occupy Cairo's iconic Tahrir Square, which was heavily guarded by security forces.

Pitched battles lasted for hours in several neighbourhoods across the capital. Most of the victims were Morsi supporters, who vowed in a statement on Monday to continue their protests, "fuelled by the precious blood and souls of the noble martyrs." They called for fresh rallies on Tuesday and Friday.

Morsi was Egypt's first democratically-elected president, and the first civilian, but he was ousted after one year in office following massive popular protests in June and July.

Also on Monday, a panel of judges recommended dissolving the Brotherhood's political wing, the Freedom and Justice Party, signaling a wider crackdown on the group.

Their recommendations will be delivered to a Cairo court reviewing a case demanding the party's dissolution on October 19.

Thousands of Morsi supporters have been killed, and more than 2,000 imprisoned, in the three months since his ouster.