The radio, citing a statement from the armed forces, said Nabil Sahrawi, leader of the Salafist Group for Preaching and Combat (GSPC), was killed by the army along with several other senior members.
The GSPC, created in 1998, claimed responsibility for the kidnapping of 32 European tourists in the Sahara desert last year. It is on the US list of foreign "terrorist" organisations.
The death of Sahrawi, who took over the GSPC leadership a year ago, was expected to significantly weaken the only remaining major organisation fighting the authorities for an Islamic state.
Algerian newspapers said Sahrawi, along with several others, was killed as part of an offensive against suspected members of the organisation following the recent killings of more than a dozen soldiers in eastern Algeria.
It said the operation was ongoing.
The daily Liberte reported that a forensic police team identified Sahrawi's body. The newspaper Le Soir said nearly 3000 soldiers were involved in the military sweep in wooded mountains in the Bejaia region of Kabylie, some 260km east of Algiers.
Armed conflict in Algeria began shortly after the army cancelled legislative elections which a now-banned Islamic party was set to win in 1992.
More than 150,000 people, mostly civilians, have since been killed, according to human rights groups.
Violence has sharply fallen over the past two years although the recent alignment of the GSPC to al-Qaida has worried analysts and diplomats, fearing a fresh wave of attacks.