Boko Haram leader Abubakar Shekau dismissed Nigerian military claims of his death in a new video obtained by AFP on Thursday and said the militants had implemented strict Islamic law in captured towns.

"Here I am, alive. I will only die the day Allah takes my breath," Shekau said, adding that his group was "running our... Islamic caliphate" and administering strict sharia punishments.

Boko Haram has shown images of extreme violence before but the latest video shows at length graphic scenes of an amputation and a stoning to death as well as a beheading.

It also purports to show the wreckage of a Nigerian Air Force jet that went missing in the northeast on September 11. Boko Haram said its fighters shot it down but the military denied the claim.

The military announced last week that Shekau was dead and that a man who had been posing as the group's leader in the videos had been killed after fighting with troops in the far northeast.

Security analysts and the United States questioned the credibility of the military's claim.

The new 36-minute video shows Shekau, in combat fatigues and black rubber boots, standing on the back of a pick-up truck and firing an anti-aircraft gun into the air.

Standing in front of three camouflaged vans and flanked by four heavily armed, masked fighters, he then speaks for 16 minutes in Arabic and the Hausa language widely spoken in northern Nigeria.

There was no indication of where or when the video was shot. Shekau appears in separate images from the violence.

The heavily bearded Shekau, who appeared to be the same man as those in previous clips, said the military's claim that he was dead was propaganda.

"Nothing will kill me until my days are over... I'm still alive. Some people asked you if Shekau has two souls. No, I have one soul, by Allah," he said, apparently reading from a script.

"It is propaganda that is prevalent. I have one soul. I'm an Islamic student.

"I'm the Islamic student whose seminary you burnt... I'm not dead," he added, apparently referring to the destruction of the group's mosque in the Borno state capital, Maiduguri, in 2009.

There have been two previous claims by Nigeria's security forces that Shekau had been killed or "may be dead" but Boko Haram has later issued denials in video messages.

Elsewhere in the new video, the militant leader said the group had implemented strict Islamic law in the towns that it had captured in the northeast in recent weeks.

"We are running our caliphate, our Islamic caliphate. We follow the Koran... We now practise the injunctions of the Koran in the land of Allah," he said.

The video showed footage a man being stoned to death for adultery, another having his right hand cut off at the wrist for theft and a man and a woman receiving 100 lashes for sex out of wedlock.

Crowds of men, women and children are seen watching the punishments.

There was again no indication of when or where the images were shot but on August 21, residents who fled the Borno town of Buni Yadi reported that the group had carried out summary executions.

The scenes of graphic violence are not unprecedented but come as other groups in the wider jihadi network, particularly Islamic State militants in Syria and Iraq, have issued similar footage.

In a Boko Haram video obtained on August 24, footage showed the apparent execution of about 20 men captured in the Borno town of Gwoza and two others beaten to death with rocks and pick-axes.

On the air force jet, Boko Haram fighters are seen apparently picking through the wreckage of the downed Alpha aircraft and the military's green and white logo is clearly visible.

But air force spokesman Air Commodore Dele Alonge told AFP: "Our plane went missing some weeks back and we are still looking for it.

"For any group to claim they shot it down is mere propaganda and rubbish."