The armed group seized 276 pupils from the Government Girls Secondary School in Chibok in April 2014.
Fifty-seven of them managed to escape in the immediate aftermath of the abduction. Some of the schoolgirls have since been released, while others managed to escape. Around 100 are still believed to be held by Boko Haram.
"We are the Chibok girls, you have been crying we should be released. But by the grace of Allah, we will not return home," one of the girls said in the undated footage, which was released on Monday.
"These people are taking care of us and we are grateful to them. We are happy here - we have found our faith," she added.
A group of about 12 girls and young women, some of whom are holding babies, are reportedly seen in the video.
Al Jazeera could not independently verify that those appearing in the video were among those abducted in Chibok.
Al Jazeera correspondent Ahmed Idris said the release of the video by Boko Haram is probably done to show Boko Haram is still a force to be reckoned with.
"The release of this particular video, according to some analysts, is to give Boko Haram an advantage in negotiations," Idris said.
"Some also believe this particular video is to show that Boko Haram is still a potent force," he added said.
"The release comes as the Nigerian military has stepped up its operations around Lake Chad and other areas in the northeast of Nigeria."
Abubakar Shekau, leader of Boko Haram, also appears in the footage, which was obtained by the Sahara Reporters website.
Sahara Reporters said they got the tape from a journalist who reports in the Lake Chad area.
In the video, Shekau claims responsibility for the downing of a Nigerian air force helicopter on January 5. The wreckage of a helicopter is also shown in the 36-minute footage.
The Nigerian government has previously said that the helicopter crashed because of a technical failure. No lives were lost in the crash.
The footage also shows clashes Boko Haram was involved in, although it is unclear who the group is fighting in the shown fragments.
Boko Haram, whose name roughly translates to "Western education is forbidden", has waged an armed campaign in northeastern Nigeria since 2009.
It initially claimed to be fighting for the creation of an Islamic state in Nigeria's Muslim north, but a range of demands by different people have since been issued.
The years-long conflict has left at least 20,000 people dead and displaced more than 2.6 million.