The senseless murder of Jordanian pilot Mouath al-Kasaesbeh by ISIS militants has been denounced by religious leaders, who are praying for interfaith unity.

Muslim clerics across the world have repeatedly condemned the violence perpetrated by jihadists, and have no expressed "deep anger" over the killing of Kasaesbeh which was revealed in a video released on Tuesday.

The captured pilot was shown apparently being burnt alive in a cage by the extremist group. Jordan, which has participated in a US-led military campaign to bomb Islamic State positions, responded overnight by executing two al Qaeda convicts on death row.

Egypt's top Muslim authority, the 1,000 year old Al-Azhar university revered by Sunni Muslims around the world, issued a statement expressing "deep anger over the lowly terrorist act" by what it called a "Satanic, terrorist" group.

The Grand Sheikh of Al-Azhar, Ahmed al-Tayeb, said the killers deserved to be "killed, crucified or to have their limbs amputated."

In Qatar, the International Association of Muslim Scholars, headed by prominent cleric Youssef al-Qaradawi and linked to the Muslim Brotherhood that has influence across the region, called the burning of Kasaesbeh a criminal act.

"The Association asserts that this extremist organisation does not represent Islam in any way and its actions always harm Islam," it said.

Islamic State posted a religious edict on Twitter, which said it is permissible in Islam to burn an infidel to death.

However, senior clerics across the Islamic world argued that inflicting death by fire was always banned under Islam.

"The Prophet, peace be upon him, advised against burning people with fire," Sheikh Hussein bin Shu'ayb, head of the religious affairs department in southern Yemen, told Reuters in Aden.

Saudi cleric Salman al-Odah wrote on his Twitter account: "Burning is an abominable crime rejected by Islamic law regardless of its causes."

"It is rejected whether it falls on an individual or a group or a people. Only God tortures by fire," he added.

Even clerics sympathetic to the jihadist cause said the act of burning a man alive and filming the killing would damage ISIS.

"This weakens the popularity of Islamic State because we look at Islam as a religion of mercy and tolerance. Even in the heat of battle, a prisoner of war is given good treatment," said Abu Sayaf, a Jordanian Salafist cleric also known as Mohamed al-Shalabi who spent almost ten years in Jordanian prisons for militant activity including a plot to attack US troops.

"Even if the Islamic State says Mouath had bombed, and burnt and killed us and we punished him in the way he did to us, we say, OK but why film the video in this shocking way?" he told Reuters. "This method has turned society against them."

The director of the Catholic Center for Studies and Media in Amman, Jordan's capital, said churches in the region are horrified at the recent events.

Special Masses and prayers are being held, as "Christian churches in the Hashemite Kingdom of Jordan convey their deep sorrow and sadness over the martyrdom of pilot Muath Kasasbeh," Father Rifat Bader said in a statement on Wednesday.

"As the churches denounce this heinous crime against humanity, they ask all citizens to reinforce their national unity under the Hashemite leadership, led by King Abdullah II," he continued.

"The churches will hold prayers as well in the first week of February for harmony among religions, so that religions will constitute a factor conducive for peace, harmony and unity among the people rather than a factor leading to division, killing, oppression and dispute."

Church bells were rung at noon on Wednesday, and dedicated services were held at 6pm.

(Additional reporting by Reuters)