The leader of Nigeria's fearsome Boko Haram has ridiculed claims that he is dead in a new video, declaring "Nothing will kill me until my days are over."

A man purporting to be Abubakar Shekau is shown standing on the back of a pick-up truck, brandishing an anti-aircraft gun which he fires into the air during a 36-minute video obtained by AFP news agency.

Flanked by four heavily-armed masked militants, Shekau says: "Here I am, alive. I will only die the day Allah takes my breath," taunting the Nigerian military which has claimed several times to have killed him.

A series of tweets from the Nigerian Army's Twitter account last Wednesday said that Shekau was "deceased" and a lookalike, Mohammed Bashir, who has allegedly been posing as the Boko Haram leader in recent videos, had also been killed.

This was later confirmed by military spokesman General Chris Okulade.

However, each time such a claim has been made Boko Haram has released a video in which Shekau – or possibly a lookalike – declares that he remains alive and in charge of the militant group.

In yesterday's video, Shekau insists that Boko Haram has created an "Islamic caliphate" in an unnerving parallel to Islamic State militants in Iraq and Syria.

"We follow the Quran...We now practice the injunctions of the Quran in the land of Allah," he says gleefully.

Shakau also claims that his followers shot down a Nigerian Air Force fighter jet that went missing on September 11, and the video shows a clip of the alleged wreckage.

The latest claims contradict rhetoric from the Nigerian government, which says it has inflicted heavy losses on terrorist groups in recent weeks.

The government has defended criticism of its slow response to Boko Haram which is thought to be responsible for over 2,000 deaths since becoming active in 2009 and has now seized control of several towns in the north-east.

On Wednesday President Goodluck Jonathan praised the army for "inflicting devastating blows at the heart of terror."

In a nation-wide broadcast to celebrate 54 years of independence from British rule, Jonathan added: "Driven by patriotic zeal, they [Nigerian soldiers] are turning the tide by their prowess and determination."