According to the reports, 42 people sustained injuries and were evacuated to hospitals in the area.
Jenin governor Talal Dweikat issued a statement reporting that 15 Palestinians were killed in the accident, all of them residents of Jenin.
Palestinian Minister of Religious Affairs Mahmoud al-Habash and the commander of the Palestinian Preventive Security Service Ziyad Hab al-Rih will be coordinating the transfer of the bodies from Jordan to the Palestinian Authority.
Palestinian President Mahmoud Abbas declared Sunday as a day of mourning.
The Israeli Foreign Ministry confirmed it had received information of the accident and Magen David Adom offered to assist with medical care.
Transportation Minister Yisrael Katz ordered the Airport Authority to keep the Allenby Bridge crossing open throughout the day, so as to allow family members of the injured to cross into Jordan.
According to the Petra news agency, the bus had most likely collided with a truck before it overturned.
The passengers were reportedly coming back from Saudi Arabia, where they had performed the Umrah pilgrimage to Mecca, the Ma'an news agency said.
Roi Kais, Shahar Chai and Attila Somfalvi contributed to this report
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