"Your alliance will not achieve anything. Amass all your weapons and face us. We welcome you," he said in a 28-minute speech, one of three videos posted by the Islamists on YouTube.
Troops from Nigeria have been backed by soldiers from Chad, Cameroon and Niger in recent weeks because of increased concerns about Boko Haram's threat to regional security.
In the second of the latest videos, images of the leader of the Islamic State group, Abu Bakr al-Baghdadi, are shown along with archive footage and a voiceover recalling a battle between British colonial soldiers and fighters from the Sokoto Caliphate in northern Nigeria.
"We never rose up to fight Africa. We rose up to fight the world," he said.
"We are going to fight the world on the principle that whoever doesn't obey Allah and the Prophet to either obey or die or become a slave."
On Sunday, Boko Haram militants waged twin attacks in the town of Diffa in southeast Niger, opening a new front in its offensive after repeated attacks in Cameroon's far northern region.
But Shekau dismissed the size of the force, which had previously been set at about 7,500.
"You send 7,000 troops? Why don't you send 70 million? This is small. Only 7,000? By Allah, it is small. We can seize them one-by-one. We can seize them one-by-one," he said in Arabic.
Shekau also directly threatened Chad's President Idriss Deby, whose forces have attacked Boko Haram in the northeast Nigerian towns of Gamboru and Malam Fatori in recent days.
Washington estimates that Boko Haram has a core of between 4,000 and 6,000 fighters but is well-equipped after raiding Nigerian Army positions.
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