A policeman and a militant were shot dead on Sunday during a fire exchange at a marketplace in Suez province, about 120 km east of capital Cairo, an Egyptian military spokesman said, Xinhua reported.
"The military forces securing Badr Markets area in Suez province were surprised by random fire shot at them by two terrorist elements, so the forces immediately replied and killed one of the terrorists while the other ran away," military spokesman Mohamed Samir said.
He noted that the clashes resulted in the death of the deputy chief of nearby police station and the injury of a military soldier.
Earlier on Sunday, two policemen were killed and three others injured as a blast targeted their armored vehicle in Arish city of Egypt's North Sinai province, according to the Egyptian interior ministry.
The attacks came one day after a policeman was shot dead and three others wounded when two unknown militants opened fire at their police vehicle on Fayoum-Cairo highway.
Egypt has been suffering anti-government armed attacks that killed hundreds of police and army men since the army removed former Islamist President Mohamed Morsi in July 2013 in response to mass protests.
Most of the anti-government attacks were claimed by "Sinai State" militant group, a Sinai-based affiliate of the Islamic State (IS) militant group.
Crackdown on Morsi's supporters since his ouster left more than 1,000 of them killed and thousands more jailed, while Morsi's Muslim Brotherhood group was blacklisted as "terrorist."
On Sunday, a criminal court in Upper Egypt's Menia province sentenced eight Brotherhood supporters to death over involvement in violence following Morsi's ouster in 2013.
The court referred their case to the country's Mufti for his non-binding religious opinion on their execution, while it delayed the trial of other 111 defendants in the same case.
The Egyptian ongoing massive security operations in the Sinai Peninsula have killed hundreds of militants as part of the country's "war against terrorism."