In a video spotted in online jihadist forums by the SITE terrorism monitoring group, Zawahiri said the new force would "crush the artificial borders" dividing Muslim populations in the region.
Al-Qaeda is active in Afghanistan and Pakistan, where its surviving leadership are thought to be hiding out, but Zawahiri said "Qaedat al-Jihad" would take the fight to India, Myanmar and Bangladesh.
"This entity was not established today but is the fruit of a blessed effort of more than two years to gather the mujahedeen in the Indian sub-continent into a single entity," he said.
Founded by Osama bin Laden, who was killed in Pakistan by US commandos in May 2011, Al-Qaeda has long claimed leadership of the jihadists fighting to restore a single caliphate in Muslim lands.
But since the death of its figurehead, it has been somewhat eclipsed, first by its own offshoots in Africa and the Arabian Peninsula, and now by the so-called "Islamic State" fighting in Iraq and Syria.
While still regarded as a threat to the West, the group has never managed to repeat the spectacular success of the September 11, 2001 attacks by hijacked airliners on New York and Washington.
But, in launching "Qaedat al-Jihad in the Indian sub-continent," Zawahiri may be attempting to recapture some of the limelight for his group and to exploit existing unrest in Kashmir and Myanmar.
"It is an entity that was formed to promulgate the call of the reviving imam, Sheikh Osama bin Laden, may Allah have mercy upon him," Zawahiri said.
Zawahiri called on the "umma," or Muslim nation, to unite around "tawhid," or monotheism, "to wage jihad against its enemies, to liberate its land, to restore its sovereignty and to revive its caliphate."
He said the group would recognize the overarching leadership of the Afghan Taliban leader Mullah Muhammad Omar and be led day-to-day by senior Pakistani militant Asim Umar.
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The 55-minute video begins with stock footage of the late bin Laden giving a sermon, before cutting to a satellite map of southwest Asia, the Middle East, the Indian sub-continent and the Horn of Africa.
Then it cuts to a white-bearded Zawahiri, in a white turban and glasses, against the backdrop of a brown floral curtain and desk with hardback books and a tin holding ballpoint pens and prayer beads.
Umar also speaks in the video -- using the Urdu language of Pakistan rather than the Egyptian doctor Zawahiri's native Arabic -- along with a new group spokesman identified as Usama Mahmoud.
The Pakistani speakers are not shown in person, and their recordings appear as a voiceover accompanying a map of India, Arabic subtitles and Islamic iconography.
The video is produced by Al-Qaeda's usual media arm, the As-Sahab Media Foundation -- "The Cloud" -- and SITE reported that it had been widely distributed on jihadist online forums.
In it, Zawahiri singles out Assam, Gujarat and Kashmir -- Indian regions with large Muslim populations -- along with Bangladesh and Myanmar, as territories targeted by the new organization.
Millions of Muslims fled India for what is now Pakistan in 1947 when the British Empire partitioned the two countries at independence, and tensions persist between those who remain and the Hindu majority.
Kashmir has an active armed insurgency against Indian rule, and there have been extremist attacks in other areas in India, most notoriously the 2008 Mumbai attacks, when four days of urban violence left 166 dead.
Indian Muslims have also been the victims of violence led by Hindu extremists. Hundreds died during the 2002 Gujarat riots, at a time when India's now Prime Minister Narendra Modi was chief minister of the state.
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Muslims are a minority in Myanmar, and the stateless Rohingya have complained of persecution by the Buddhist majority.
Zawahiri called on Muslims living in the sub-continent -- "which was once part of the lands of Muslims, until the infidel enemy occupied it and fragmented it" -- to support their "mujahedeen brothers."
And he urged them to reject the "deceptive mirage" of secular democracy in favor of religious government and sharia law.
Zawahiri is still the United States' most wanted fugitive for his role in Al-Qaeda, first alongside bin Laden and since his death as its leader.
The State Department "Rewards for Justice" program has placed a $25 million bounty on the 63-year-old's head and US drones still patrol above the Afghan-Pakistan border area where he is thought to be.