In his voice message, Abubakar Shekau, Boko Haram's leader, had said his militia was behind Friday's nighttime kidnapping, an online newspaper reported on Tuesday.
At least 333 pupils were missing from the all-boy Government Science Secondary School at Kankara town in northwest Katsina state, its governor Aminu Bello Masari said on Sunday.
Katsina is the home state of Nigerian President Muhammadu Buhari, who has made the fight against the Islamist group a priority.
His spokesman Garba Shehu said on Monday that the "kidnappers had made contact," adding that negotiations over the children's "safety and return" were taking place.
Governor Masara said: "We are making progress and the outlook is positive," after talks with Buhari, who was visiting his home state.
'Un-Islamic practices'
Without further independent verification being provided, the online newspaper quoted Shekau as saying: "What happened in Katsina was done to promote Islam and discourage un-Islamic practices such as Western education."
Kankara residents told the French news agency AFP that gunmen on motorcycles stormed the rural school. A number of boys escaped, but many were captured.
Friday's raid evoked memories of the 2014 kidnap of more than 200 girls from a school in Nigeria's northeastern town of Chibok by Boko Haram.
Since then, about half of those girls have been found or freed, and an unknown number are believed to have died.
Mounting public anger over Nigeria's precarious security situation grew Monday as the hashtag #BringBackOurBoys trended on Twitter, an homage to the #BringBackOurGirls appeal of 2014 and beyond.
Late last month, Islamist militants killed scores of farmers in northeastern Borno, beheading some of them.