Retired air chief marshall Alex Badeh was shot dead last week by unknown gunmen on a road outside Abuja, the nation's capital.

He was returning from his farm when he was ambushed and shot dead.

The police said in a statement they had arrested "two principal suspects who participated in the killing... and three other suspects."

"They are now in police custody undergoing investigation."

Describing the killing as "very sad and unfortunate," Nigerian President Muhammadu Buhari immediately ordered the security forces to arrest the killers to bring them to justice.

He also ordered the police to ensure greater security and safety of drivers.

Badeh, 61, who served as Nigeria's defence chief under former president Goodluck Jonathan, retired in 2015. He has been on trial since then over allegations of corruption while in office.

Nigeria, Africa's most populous nation, is battling a myriad of security problems, from Boko Haram jihadists in the northeast to farmer-herder conflict in the centre and kidnappings for ransom and armed robberies in the south.

Buhari who came to power in 2015 and is seeking a second term in February elections, has come under fire for not doing enough to address the security challenges.