A video has been posted online by the extremist group appearing to show Lt Moaz al Kasasbeh being locked in a cage and burnt alive.
"We are used to terrible things here in the Middle East but the murder of the Jordanian pilot by burning him to death on camera is just the most terrible thing I have ever seen," said Canon White, who was once the only Anglican vicar in the Iraqi capital.
"All we can do is say 'Lord Have Mercy'," he added.
The Jordanian pilot was captured by IS when his plane crashed near the town of Raqqa in Syria in December.
Jordan has been involved in the US led airstrikes on Islamic State.
It was hoped the pilot's life could be saved in a prisoner transfer with IS. The terrorist group had wanted would-be suicide bomber Sajida al-Rishawi released in exchange for Lt Moaz al Kasasbeh.
Jordan had agreed to the deal but IS could not provide proof he was still alive and officials have said they now believe he was murdered a month ago.
This morning the country executed her and another prisoner with links to IS in response to the killing of the pilot.
Prime Minister David Cameron has condemned the killing of Lt al Kasasbeh as a "sickening murder".
He said: "I pay tribute to the dedication and bravery of Lieutenant Moaz al Kasasbeh, who as a member of the Jordanian Armed Forces serving in the anti-ISIL Coalition, paid with his life while protecting his country and us all.
"My thoughts and prayers are with his family tonight at this tragic time."
Earlier this month the Latin Patriarch of Jerusalem visited the family of the man.
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.
