The video posted online shows Wuhayshi addressing scores of jihadists in a rugged terrain as he welcomes 19 militants who escaped a Sanaa prison in February.
"We will continue to raise the banner of Islam in the Arabian Peninsula and our war against the crusaders will continue everywhere in the world," he says in the video.
Al-Qaeda usually uses the term crusaders to refer to Western powers, especially the ones which have intervened militarily in Muslim countries, mainly the United States, Britain and France.
Some of the former inmates describe in the video how they escaped the prison.
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In a brazen two-pronged jailbreak, AQAP militants slammed a car bomb into the eastern gate of a Sanaa prison as others attacked the guards at its main entrance.
The attack allowed 29 inmates to escape, including the 19 jihadists.
Wuhayshi vowed last August to free incarcerated members of his group.
He himself escaped in February 2006 from the political security prison in Sanaa along with 22 other members of AQAP.
AQAP took advantage of the weakening of the central government in Sanaa after a popular uprising in 2011 forced president Ali Abdullah Saleh from power early the following year.