Two Egyptian soldiers were shot dead Friday trying to arrest a leader of an Al-Qaeda inspired group spearheading an insurgency in the Sinai, the military said.
Elsewhere, police arrested 85 Islamist protesters as they dispersed rallies demanding the reinstatement of ousted president Mohamed Morsi, the interior ministry said.
The country is still reeling from near daily protests as well as militant attacks in the Sinai peninsula following the military's overthrow of Morsi in July.
The two soldiers were killed as they came under fire during an operation to arrest Shadi al-Menei, reportedly the leader of Ansar Beit al-Maqdis, the military spokesman said.
The group, inspired by Al-Qaeda, has claimed some of the deadliest attacks in an insurgency in Sinai that has killed dozens of soldiers and policemen.
Three "terrorists" were killed in the gunfight, said Colonel Ahmed Ali in a statement, adding that helicopters were "currently dealing with the targets."
Based in the sparsely populated and desert north of the peninsula, which borders Gaza and Israel, the militants have pressed their attacks despite a massive army deployment.
The army has announced the killing or capture of several militant leaders, but Menei has so far eluded them.
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Across the country, police on Friday clashed with protesters who rallied in several cities in support of Morsi, firing tear gas to disperse them.
The interior ministry said police arrested 85 protesters in seven cities, adding eight policemen were wounded in Cairo clashes.
A health ministry official said one person was critically wounded in clashes between protesters and police in the canal city of Suez.
Morsi's supporters hold almost daily protests and organise larger rallies on Fridays, despite a crackdown that has killed more than 1,000 people in clashes and imprisoned thousands more since his overthrow.
Prosecutors and police have alleged ties between militants in the Sinai and Morsi's more moderate Muslim Brotherhood movement, charges the Brotherhood denies.
Morsi and 35 Islamists, including the Brotherhood's senior leadership, will stand trial for colluding with Palestinian and Lebanese militants to conduct "terrorist" acts, the prosecution said this week.
Morsi, detained since his ouster, is already on trial for allegedly inciting the killings of opposition protesters during his year in power.
Egypt's first democratically elected president, Morsi quickly alienated a secular opposition, the police and the powerful military, which toppled and arrested him following mass protests demanding his resignation.
The military-installed interim government last month banned all but police-sanctioned protests.