According to an unverified audio clip, the group - whose name means "Western education is forbidden" - was responsible for last week's raid on an all-boys school in the town of Kankara in northwestern Katsina state.

Parents fear time may be running out: Boko Haram has a history of turning captives into jihadist fighters.

"They will radicalize our children if the government does not act fast to help us rescue them," said trader Shuaibu Kankara, crying as he spoke from home.

His 13-year-old son, Annas, was among those abducted from the Government Science school on Friday night.

Two other sons managed to escape, he added, when men on motorbikes with AK-47 assault rifles stormed the school and marched the boys into a forest.

Some experts feared the boys could be taken over the border into Niger or at least split into groups to make finding them harder.

Late on Wednesday, Katsina state Governor Aminu Bello Masari told the BBC Hausa service that the estimated 320 missing boys were in the forests of neighboring Zamfara state.

Earlier in the day, an aide to Masari said soldiers and intelligence officers had been combing the Rugu forest, which stretches across Katsina, Zamfara, Kaduna and Niger states, in search of the boys.

Boko Haram and its offshoot, Islamic State West Africa Province, have waged a decade-long insurgency estimated to have displaced about 2 million people and killed more than 30,000. They want to create states based on their extreme interpretation of sharia law.

If Boko Haram carried out the kidnapping in an area where it had not previously claimed attacks, it would mark an alarming expansion beyond its northeastern base, security experts say. But it may alternatively have purchased the boys from criminal gangs in the northwest with which it has been building ties.

Vincent Foucher, a security analyst at the French National Center for Scientific Research, said Boko Haram earlier this year released videos in which it said groups in the northwest had pledged allegiance to its movement.

The abduction echoes Boko Haram's 2014 kidnapping of more than 270 schoolgirls in the northeastern town of Chibok. The attack gave rise to a global #BringBackOurGirls campaign.

Six years on, only about half the girls have been found or freed. Others were married off to fighters, while some are assumed to be dead.

"We pray it's not going to be another situation of the Chibok girls' abduction," said Ahmed Bakori, a farmer whose 14-year-old son, Abubakar, was among those taken.

About two dozen parents came to the Government Science compound on Wednesday and prayed in the school mosque. The compound, composed of white single-story buildings built on dusty red soil, was quiet.

Abubakar Lawal, who has two children among the captives, said he did not believe Boko Haram's claim and would wait with patience and prayers. "The government has to do diplomacy in a way to rescue these people," he said outside the school.

The attack is awkward for President Muhammadu Buhari, who comes from Katsina and arrived on a private visit hours before the kidnapping. Buhari has repeatedly said that Boko Haram has been "technically defeated."

A former military ruler, Buhari was elected in 2015 in large part due to his pledge to crush the insurgency. Under his predecessor, Goodluck Jonathan, Boko Haram grew in strength and controlled territory around the size of Belgium.

Across the nation, anger and anxiety were building over the abductions, with #BringBackOurBoys trending on Twitter.

Military spokesman John Enenche said troops were determined to rescue the boys alive and had no evidence any were dead.

He gave new details of the school attack and subsequent firefight with guards. Soldiers arrived but could only shoot in the air as the assailants used the boys as shields.

Jacob Zenn, a Boko Haram expert at the US-based Jamestown Foundation think tank, said the longer the boys were with their captors, the likelier their indoctrination would be. He cited the example of some Chibok girls who chose to stay with Boko Haram.

"The longer this goes on, the more pressure will grow on the government to negotiate, and the more leverage the militants will have over the government," he added.