Two people were killed in the town of Tammun, said Ahmad Assad, governor of the nearby city of Tubas whose jurisdiction includes Tammun.
"There is a martyr from the air strike whose body is torn to pieces," he told AFP.
The Palestinian health ministry in Ramallah confirmed two men had been killed by Israeli forces in Tammun.
"The body of one of them, whose identity is still unknown, has been withheld by the army," the ministry said in a statement.
Two other Palestinian men were killed in another Israeli air strike in the town of Qabatiyah, near the northern West Bank city of Jenin, the governor of Jenin said.
"Two martyrs were killed as a result of an air strike carried out by Israeli forces during an operation in the Qabatiyah area," the governor, Kamal Abu Rubb, told AFP.
The two men were aged 40 and 38 and were related, he added.
Violence in the West Bank, particularly in the northern areas of the territory, has soared since the war in Gaza broke out on October 7 last year.
SD/