Yousafzai, who has become an international symbol for women's rights in the face of hard-line Islam, said Nigeria's president promised to meet for the first time with the abducted girls' parents.
"My birthday wish this year is 'Bring Back Our Girls' now and alive," she said, using the social media slogan that has been picked up around the world to demand freedom for the girls, who were abducted in April by the extremist group Boko Haram from a school in the remote northeast Nigerian town of Chibok.
"Lay down your weapons. Release your sisters. Release my sisters. Release the daughters of this nation. Let them be free. They have committed no crime."
She added: "You are misusing the name of Islam ... The Quran teaches brotherhood."
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Malala also spoke against the custom of child brides in her home country, a tradition common in Nigeria, too. Boko Haram has threatened to sell some of the girls as brides if its fighters are not freed.
"Protect girls from cruelty," she said in her annual Malala Day speech, saying girls should not be forced to marry or to leave school to become brides "when they should be girls," or to give birth to children "when they themselves are children."
Gunmen destroyed most of the bridge on the road between Maiduguri and Biu on Saturday night, making it impossible for vehicles to cross, the spokesman for the Nigerian Vigilante Group, Abbas Gava, told The Associated Press.
Malala met today with Nigeria's President Goodluck Jonathan and told reporters that the president "promised me that the girls will be returned as soon as possible."
"I could see tears in their eyes. They were hopeless. But they seem to have this hope in their hearts," and they were asking if they could meet the president.