"They do face a very vicious terrorist organisation in terms of Boko Haram, they are investing in and training their armed forces and counter-terrorism abilities," Prime Minister David Cameron told MPs.
"We have worked with them on that and we are willing to do more work with them on that, particularly if we can make sure that proper processes are in place for dealing with human rights areas.
Cameron was responding during Prime Minister's Questions to Labour MP Tom Clarke, who said the Nigerian government had "not lifted a finger to protect its own citizens in the north".
But Cameron insisted the Nigerian authorities were trying to tackle Boko Haram.
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The Military of Defence confirmed the surveillance aircraft offered to Nigeria was a RAF Sentinel R1 spy plane.
The schoolgirls were taken by Islamist militants Boko Haram on April 14.
Experts from the UK have already been sent to help with the search for the 200-plus schoolgirls, who were taken from their boarding school in the town of Chibok in north-eastern Nigeria.
The US has already sent surveillance assistance and has teams helping on the ground in Nigeria.
More than 270 girls were snatched by militants from their boarding school in Chibok, north-eastern Nigeria, on April 14. Some managed to escape, but most were taken into the remote Sambisa forest.
In the video, the Boko Haram leader, Abubakar Shekau, said the girls could be released in exchange for jailed militants.
Boko Haram, whose name means "Western education is forbidden", had previously said the girls should not have been at school and should get married instead. The militants have been engaged in a violent campaign against the Nigerian government since 2009.