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A power struggle within Nigeria's Islamic State group affiliate Boko Haram has gone public and threatens to destroy the militants.

Two men claiming to be the rightful leaders of the West African extremist group have released videos and audio statements belittling their rivals and staking their claim for leadership of the group.

Abu Musab al-Barnawi was named by the Islamic State group as the new governor of its West Africa Province last week.

He alleges that the group's leader Abubakar Shekau has targeted "fellow Muslims" and killed his own fighters. 

Barnawi also said that Shekau lives a life of luxury while his fighters' children starve.

Militants themselves remain hungry and underequipped for battle with Nigerian government forces, he added.

Shekau responded in a video posted on YouTube posted on Sunday night but which was quickly taken down.

It begins with a masked man in front of a group of militants saying they refused to follow Barnawi and described Shekau as "our leader".

We have not reneged on our loyalty to the leadership of [Abu Bakr] al-Baghdadi. -Abubakar Shekau

Shekau appears saying that Barnawi is not qualified to lead the group and that he remained Boko Haram's legitimate chief. 

"We have not reneged on our loyalty to the leadership of (Abu Bakr) al-Baghdadi [IS leader]," he said. 

Shekau then fires his rifle into the air and is flanked by two fighters holding grenade launchers.

"President (Muhammadu) Buhari, very soon you will see us inside your home, the presidential palace," Shekau threatens.

It follows an audio statement by Barnawi claiming that eight members of Shekau's "kitchen Cabinet" had revolted.

He also said that he had implanted followers within the Shekau's bodyguard ready to kill him if he is killed first.

Shekau had lost the support of the Islamic State group because of his current tactic of killing Muslims indiscriminately, including suicide bombings and shootings targeting mosques, Barnawi said.

"You will see how he (Shekau) justifies and boasts of killing people. We are not killers like him," Barnawi adds.

The claimant of Boko Haram's leadership vowed to continue attacks against Christians and churches but promised not to attack mosques or markets frequented by Muslims.

What is certain is that the current in-fighting won't help the group which has suffered a series of setbacks following successes from a multinational force in northeast Nigeria.

Boko Haram have been forced to scaleback their attacks this year, but the damage remains, with more than 20,000 people killed in fighting, 2.2 million forced from their homes, and hundreds of hostages - including school children - held by the militants.

Agencies contributed to this story.