Samir Mousaab was killed near the village of Si Moustapha about 25 miles east of the capital, Algiers, the radio reported.
It said Mousaab's body was identified by former members of the Salafist Group for Call and Combat, an insurgent group that changed its name to al Qaeda in Islamic North Africa when it announced its alliance with al Qaeda in January.
The group was built on the foundations of an Algerian insurgency to topple Algeria's secular government that erupted in 1992 after the army canceled elections that a Muslim fundamentalist party was set to win.
Up to 200,000 people — militants, security forces and civilians — have been killed.
Thursday's clash came weeks after double-suicide bombings on April 11 that killed 33 people and wounded 57 in Algiers. Al Qaeda in Islamic North Africa claimed responsibility for the attacks, coordinated suicide bombings targeting the prime minister's office and a police station.
The attacks were the deadliest in the Algiers region since 2002, when a bomb in a suburban market killed 38 people and wounded 80.
Algeria has tried to turn the page on the insurgency through military crackdowns and amnesty offers. Until recently, its efforts appeared successful, with militants' ranks decimated and the holdouts isolated in rural hideouts.
Reassured, foreign businesses returned to oil- and gas-rich Algeria, and many foreign workers moved out of hotels and into apartments.
Yet violence has surged again recently, and al Qaeda's North Africa wing has claimed responsibility for several recent attacks on foreigners.
A March 3 bombing of a bus carrying workers for a Russian company killed a Russian engineer and three Algerians. In December, an Algerian and a Lebanese citizen were killed in an attack that targeted a bus carrying foreign employees of an affiliate of the U.S. company Halliburton.