President Buhari condemned the attack on his home state in a statement on Saturday, assuring the police would deploy additional resources to aid the search and rescue.
"Our prayers are with the families of the students, the school authorities and the injured," he added.
Police are working with the army and the air force to determine the exact number of students missing as desperate parents gathered at the school to begin a search for their children.
Bint'a Ismail, a parent of one of the abducted children, slammed the governments response: "Sincerely speaking, we here in Katsina State are in a terrifying condition.We don't see the value of the Government in fact.
"I have a younger brother and a child taken along by the kidnappers. I have been in this school since dawn and yet there is no update."
The state of Katsina is plagued by attacks from "bandits", who regularly attack locals and kidnap people for ransom.
The school siege comes just a month after scores of farmers were killed, some even beheaded, by Islamist militants in the north-eastern Borno state.
The rebels are common in north-eastern parts of Nigeria.
No groups have yet claimed responsibility for the kidnapping in Katsina.
The incident echoes the 2014 kidnapping of more than 270 girls by militant Islamist group Boko Haram from a school in Chibok, north-eastern Nigeria.
The governor of Katsina, Aminu Bello Massari, has ordered the immediate closure of all boarding schools in the state.
President Buhari was due to brief the national assembly on the security situation last week, but cancelled the appearance without official explanation.
He arrived in his home village, around 125 miles from Kankara, on Friday for a week.
The school is located in President Buhari's home state Credit: Reuters Police and military have located the kidnappers in a jungle Credit: Reuters