Two members of the Muslim Brotherhood were killed in an exchange of gunfire with Egyptian security forces in the Nile Delta on Friday, Reuters reported the Interior Ministry as saying, and the Islamist group said another of its supporters was shot dead in Alexandria Al Arabiya reported.
Meanwhile in Sinai, Egyptian soldiers killed a prominent militant in the restive peninsula where Islamist fighters have increasingly targeted security forces since the ouster of President Mohammed Mursi last year, Agence France Presse reported.
The Interior Ministry said the Nile Delta shootout began when Brotherhood activists on motorbikes were spotted attempting to set alight a police checkpoint on a road between the cities of Tanta and al-Mahalla al-Kubra north of Cairo, Reuters reported.
They opened fire on police as they tried to flee, the statement said.
"The forces encircled them and took the necessary security measures and exchanged fire. That led to the death of two of them," the ministry said in a statement. Three others were arrested, it added.
The Brotherhood had no immediate comment on the incident, the news agency said.
Reuters said the death in Alexandria was confirmed by senior ambulance service official Omar Nasr.
The website of the Brotherhood's Freedom and Justice party identified the man killed as 50-year old Abdel Hakim el-Zamzami, according to the news agency. The site said he had been shot by security forces and "militias" as they tried to break up a protest.
The incidents in Cairo and Alexandria come a day after Egypt issued a decision to speed up the implementation of legal penalties against the Muslim Brotherhood after it was blacklisted as a terrorist group months ago, Ahram Online reported.
The interim government urged for enforcing legal penalties against anyone who is a member of the Muslim Brotherhood, any person who supports it verbally or in writing or in "other ways" and any person who funds its activities, the English-language website said.
Also, Arab states subject to the 1998 Arab Convention on the Suppression of Terrorism will be notified of the decision.
Meanwhile in the Sinai Peninsula, Egyptian soldiers killed Nour al-Hamdeen, "one of the most prominent and dangerous extremists," military spokesman Colonel Ahmed Ali said in a statement, according to AFP.
Hamdeen was ambushed by soldiers on a road to Al-Tuma village in northern Sinai, and was killed in the ensuing firefight, the statement said.
The army has poured troops into the mountainous and underdeveloped Sinai bordering the Palestinian Gaza Strip and Israel, to combat growing militancy.