Boko Haram called on the government to release their fighters in exchange for the girls who were kidnapped in April 2014.
A father of one of the 218 girls still missing said he recognized his daughter in the video, as a spokesman for the Bring Back Our Girls movement said he was "certain" of the identities of 10 other girls seen in the footage.
The Nigerian government said it was in touch with those claiming to be behind the undated video, which shows a group of approximately 50 girls in Islamic dress sitting and standing around a masked man armed with an assault rifle.
The film was issued just days after embattled Boko Haram head Abubakar Shekau denied claims he had been replaced as the leader of the Nigeria-based jihadist group.
A man wearing camouflage gear in the video called on the government to release Boko Haram fighters in exchange for the girls who were kidnapped in April 2014.
"They should immediately release our brethren in their custody," the man said, warning that if the prisoners were not released the government would never be able to rescue the girls.
While President Muhammadu Buhari has said the group is "technically defeated", his government has struggled to find the girls, an enduring political embarrassment that highlights Boko Haram's continued presence in the region.
- '40 girls married' -
The mass kidnapping of schoolgirls from the remote town of Chibok provoked global outrage and brought unprecedented attention to Boko Haram and its bloody quest to create a fundamentalist state in northeastern Nigeria.
The new video was attributed to the original Boko Haram name, not the new Islamic State West Africa Province (ISWAP), suggesting it was released by Shekau's faction, although it is not known when or where it was filmed.
"There are a number of the girls, about 40 of them, that have been married," said the man in the 11-minute video. "Some of them have died as a result of aerial bombardment."
A girl who gave her name as Maida Yakubu speaks in the Chibok dialect and chokes back tears as she describes an air strike by Nigerian armed forces.
In the background, several girls look visibly distressed and dab their eyes. One is holding a small baby.
"When I heard her voice, I realised she is my daughter," her father Kanu Yakubu told reporters in Abuja.
"We're certain that these are the Chibok girls," Bring Back Our Girls spokesman Abubakar Abdullahi told AFP.
"We recognise up to 10 from the video," Abdullahi said, adding that he was waiting for confirmation from the Nigerian government and parents of the girls before releasing more names.
- 'Sense of desperation' -
"This focuses on using the girls as a bargaining chip," Ryan Cummings, director at intelligence firm Signal Risk, told AFP.
"The video shows that the war effort is hurting the operations of the group," he said. "It does have a sense of almost desperation from Boko Haram."
The Nigerian government said it is in contact with those claiming to be behind the video but was acting cautiously given the leadership split.
"Since this is not the first time we have been contacted over the issue, we want to be doubly sure that those we are in touch with are who they claim to be," Information Minister Lai Mohammed said in a statement.
Last week, the shadowy Shekau appeared in a video vowing to fight on, shrugging off an apparent split after he was said to have been replaced by Islamic State-backed rival Abu Musab al-Barnawi.
Barnawi has criticised Shekau's indiscriminate and brutal leadership in Nigeria that has seen Boko Haram fighters kill thousands of people in mosques and markets and raze entire towns.
In March 2015, Shekau pledged allegiance to the Islamic State and changed Boko Haram's name to ISWAP, prompting fears the Nigerian insurgency would be bolstered by its connection to the global jihadists.
However, there have been few signs that Boko Haram has benefited from the alliance, as the Nigerian military recaptures territory once controlled by the insurgents.
Over the past year, the military has announced the rescue of hundreds of people, most of them women and children, who were kidnapped by Boko Haram.
But the missing Chibok girls have not been among them, despite several unconfirmed sightings.
Boko Haram has been blamed for some 20,000 deaths and displacing more than 2.6 million people since it launched a brutal insurgency in Nigeria in 2009 that has since spread into several neighbouring countries.
Watch the original video released by Boko Haram below.