Two relatives of the pilot, Flight Lieutenant Moaz Youssef al-Kasasbeh. said they had been told by the head of the Jordanian air force that the claims were accurate. The Jordanian army said: “Jordan holds the group and its supporters responsible for the safety of the pilot and his life.”
The British-based Syrian Observatory for Human Rights monitoring group said it had confirmed reports the plane was brought down near Raqqa, an IS stronghold in north-eastern Syria.
The reports are difficult to verify, but IS has not managed to shoot down a coalition plane since air strikes began in August.
Islamic State has published pictures which allegedly show the pilot being held. He is said to have been taking part in coalition air strikes against the militants in Syria.
The Syrian government and US-led coalition regularly bomb IS targets in Raqqa province, which borders Turkey.
Saudi Arabia, Qatar, Jordan, Bahrain and the United Arab Emirates have participated in or supported the strikes against IS targets in Syria, according to US Central Command.