A bomb also exploded on a bridge leading to the upscale Cairo district of Zamalek, which hosts many embassies, killed one policeman
Islamist militants hit Egypt's two largest cities on Sunday with a bombing in Cairo and an attack on a church in Alexandria, leaving one policeman dead and seven people wounded, security sources said.
In a separate incident, the leader of a militant group that has targeted police and soldiers around the capital was killed in a firefight with security forces early on Sunday, the interior ministry said.
Egypt is facing an insurgency based in North Sinai that has killed hundreds of soldiers and police since the army toppled Islamist president Mohamed Mursi in 2013 following mass protests against his rule.
Most militant attacks have taken place in the Sinai Peninsula, a remote but strategic region bordering Gaza, Israel and the Suez Canal. Smaller-scale bombings have become increasingly common in Cairo and other cities.
A bomb explosion on a bridge leading to the upscale Cairo district of Zamalek, which hosts many embassies, killed one policeman, the interior ministry said. Two more officers and a civilian were injured.
The force of the bomb, which the sources said was planted in or near a car, left a shallow crater and pools of blood on the 15 May Bridge.
In Alexandria, militants in a micro bus shot at the Church of the Angel Rafael, wounding one police officer and three civilians before fleeing, security sources said.
On Saturday, two bombs exploded near a police station in the residential Imbaba district across the Nile River from Zamalek, causing no casualties.
Sunday's bombing was claimed on Twitter by Ajnad Misr, a militant group that emerged in January 2014 and has targeted security forces in and around Cairo.
"God has enabled our brave soldiers to plant an IED where the criminal (security) services were gathered on the bridge," Ajnad Misr's media wing said.
In a separate incident, the founder and leader of Ajnad Misr was killed by security forces, security sources said.
Hammam Mohamed Ahmed Attia of Ajnad Misr was shot dead during a clash around 1 a.m. (2300 GMT) at an apartment in Giza, a suburb of the capital, the security sources said.
The interior ministry said in a statement that under his leadership, the group had launched 26 attacks on police and soldiers.
Security sources say the group is guided by a conservative Salafist Islamist ideology but it is not believed to have ties to al Qaeda or the Egyptian affiliate of ISIL, Sinai Province.
Sinai Province has claimed responsibility for much of the violence wracking the Sinai, while Ajnad has focused more on the greater Cairo area.
In North Sinai, a soldier was found dead with a gunshot wound to the head, apparently executed after militant attacks on Thursday that security sources said killed 17 soldiers and three civilians. The army was not immediately available for comment.