"I direct a message to our generous brothers of the Islamic State in Syria: to host my son, the pilot Maaz, with generous hospitality," he said.
"I ask God that their hearts are gathered together with love, and that he is returned to his family, wife and mother."
He added that his son's mother was in a state of breakdown.
Isis jihadists sought to turn the event into a propaganda coup, publishing photographs on pro-Isis websites, showing its fighters holding the captured pilot.
One showed Kaseasbeh, wearing only a white shirt, being carried from a body of water by four men.
Another showed him on land, surrounded by about a dozen armed men.
Pro-Isis Twitter accounts published a photo showing a trail of white smoke plummeting to earth and claiming the jet had "suddenly lost altitude" and that they had then hit it with a shoulder-launched missile.
Amaq News Agency, a pro-Isis outlet, identified the village where the Jordanian jet was shot down as Hamrat Ghnam, in the eastern part of Raqqa's countryside.
The US Central Command, which oversees the coalition air war over Iraq and Syria, said: "Evidence clearly indicates that [Isis] did not down the aircraft as the terrorist organisation is claiming."
The statement did not give a cause for the crash, but confirmed the pilot had been taken captive by Isis guerrillas.