A group of 21 children who were abducted by gunmen on October 30 from a farm in northwestern Nigeria's Katsina state were freed and reunited with their families on Sunday, police said.

Kidnapping has become endemic in recent years in Katsina - the home state of President Muhammadu Buhari - as roving gangs of armed men abduct people from schools, hospitals, roads and farms and demand ransom cash from their relatives.

Three of the captives' parents told reporters that the children, aged between 8 and 14, were released after parents paid a ransom of 1.5 million naira ($3,400), but police spokesperson Gambo Isa denied a ransom had been paid.

"They have been reunited with their families," Isa said in a message shared via ­WhatsApp late on Saturday.

The three parents who spoke to reporters asked not to be named.

"They said if we don't pay the ransom between 4 pm and 5 pm yesterday [Saturday] they will move into the deep part of the forest with them and then we will never see them," one father said, adding that some parents had to turn to relatives to help raise their share of the money.

Parents said more than 30 children were kidnapped on October 30 while harvesting crops at a farm located between Kamfanin Mailafiya and Kurmin Doka villages in Katsina, but some managed to escape.

The farm manager had previously struck a deal with the bandits, who demanded protection money to let the harvest go ahead and were given a down payment, officials said.

Police and the parents said all the remaining captives were now free.