Boko Haram leader Abubakar Shekau indicated in a video this week that he could release the 223 girls now held for more than a month in exchange for militant fighters in custody in Nigerian jails.
But Britain's Africa minister Mark Simmonds said after meeting President Goodluck Jonathan on Wednesday that the head of state was adamant there "will be no negotiation that involves a swap".
Ayuba Chibok, whose niece is among the hostages, said the girls' detention was taking its toll on parents and families in their remote town from where the teenagers were abducted on April 14.
"Let (Shekau) release these girls unconditionally," he added.
The mass abduction -- and Boko Haram claims that the girls would be sold as slaves -- has led to global outrage and galvanised the international community to help Nigeria end the crisis.
US drones and manned surveillance aircraft have been deployed, the Pentagon said, while Britain was sending a spy plane and a military team to Abuja to work alongside French and Israeli experts.
Jonathan has called the security situation in the region "daunting" and said he was concerned by the mounting loss of life among civilians.
Boko Haram, which wants to create an Islamic state in Muslim-majority northern Nigeria, has been fighting an increasingly deadly insurgency since 2009 which has claimed thousands of lives.
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