Lt Mu'ath al-Kaseasbeh was taken after his F-16 fighter jet crashed near Raqqa, Syria on Christmas Eve.
Patriarch Fouad Twal joined representatives of Jordanian churches when he met with the Al-Kaseasbeh family in the country.
The visit was intended to show support for the many Muslims who are joining the fight against Islamic State.
IS militants have been taking over large parts of Iraq and Syria and forcing tens of thousands of Christians to flee their homes.
Safi Yousef al-Kaseasbeh, the pilot's father, met with the clergyman at his home in Karak, south of Amman, Jordan on Saturday.
He had earlier appealed for his son's captors to show mercy: "May Allah plant mercy in your hearts and may you release my son."
Islamic State claims to have shot down the plane although this has not been confirmed.