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"He made it very clear that there would be no negotiations with Boko Haram that involved a swap of abducted schoolgirls for prisoners," Mark Simmonds told a news conference.
The Islamist group, which is holding more than 200 girls, posted a video on Monday offering to release them in exchange for prisoners held by the government.
Boko Haram militants, who are fighting for an Islamist state, stormed a secondary school in the northeastern village of Chibok on April 14 and seized 276 girls who were taking exams. Some have managed to escape, but about 200 remain missing.
The abductions have triggered a worldwide social media campaign under the Twitter hashtag #BringBackOurGirls, and prompted the United States, Britain, France and Israel to offer help or send experts to Nigeria.
Britain offered further help to Nigeria including a surveillance plane and the offer was accepted, Simmonds said.