Meanwhile, Boko Haram has claimed responsibility for the abduction of the students – more than 300 boys – from northern Katsina State.
Local authorities in Nigeria have said "talks" are under way with kidnappers who have seized hundreds of students, an attack claimed by Boko Haram.
"The abductors of our children have made contacts with the government and talks are ongoing to ensure their safety and return to their respective families," Aminu Bello Masari, the governor of Katsina state, said on Twitter late on Monday.
At least 333 boys are missing after heavily armed men attacked their boarding school in the town of Kankara on Friday.
"I am Abubakar Shekau and our brothers are behind the kidnapping in Katsina," the leader of Boko Haram said in a voice message.
More than 100 gunmen on motorcycles stormed the rural school north of Kankara town, forcing students to flee and hide in the surrounding bush.
A number of boys were able to escape, but many were captured, split into groups and taken away, residents told AFP.
#BringBackOurBoys has been trending on social media since the weekend in reference to a similar hashtag used after Boko Haram abducted 276 girls in 2014 in Chibok in northeastern Nigeria.
The weekend attack was initially blamed on armed groups locally known as "bandits", who are active in the unstable region where kidnappings for ransom are common.
The government said a joint rescue operation was launched on Saturday by Nigeria’s police, air force and army after the military engaged in gunfights with bandits after locating their hideout in the Zango/Paula forest.
The kidnappings occurred in the home state of President Muhammadu Buhari, who condemned the attack and ordered security stepped up in schools. In Katsina, all schools were closed.
Tuesday's claim of responsibility marks a major turning point in the advance of militant groups in northwest Nigeria.
Boko Haram, and a splinter group, the Daesh affiliate in West Africa Province, are waging an insurgency in the northeast of Nigeria and are thought to have only a minor presence in the northwest.
But concerns have grown of militant inroads into the region, especially after fighters claiming to be in the northwest released a propaganda video pledging allegiance to Abubakar Shekau earlier this year.
READ MORE: Nigeria steps up efforts to rescue abducted students
'Hit me repeatedly'
Angry residents heckled the Katsina state governor during a visit to the area on Saturday, while protesters greeted a government delegation led by Defence Minister Bashir Salihi-Magashi on Sunday.
Osama Aminu Maale was one of the students who escaped the abductors and returned to his parents.
"There were a total of 520 of us that were taken by the gunmen from the school," the 18-year-old student told AFP by telephone at the weekend.
"After they took us away we stopped inside the bus where they made the older students take a headcount. We counted 520," he said.
The hostages were split into groups before Maale and four others escaped.
"One of the gunmen hit me repeatedly when I failed to keep up with the rest of the group due to my failing health before he let me trail behind, giving me the chance to escape," he said.
READ MORE: Five years on more than 100 Chibok girls still missing
Deteriorating security situation
The Boko Haram insurgency began in 2009 in northeastern Nigeria before spreading to neighbours including Niger, Cameroon and Chad.
Since then, more than 36,000 people have been killed in Nigeria and two million forced to flee their homes, sparking a humanitarian crisis in the region.
Boko Haram carried out the 2014 kidnap of more than 200 girls from a school in the northeastern town of Chibok. Since then, about half of those girls have been found or freed, dozens have been paraded in propaganda videos, and an unknown number are believed to have died.
Buhari has made the fight against Boko Haram a priority of his adminstration, but the security situation in northern Nigeria has deteriorated since his 2015 election.
A regional military coalition has been formed to fight the insurgents.
READ MORE: Women of war — Boko Haram wives