Jordanian protesters hold up pictures of Jordan's King Abdullah and Jordanian pilot Muath al-Kasaesbeh, as they chant slogans during a march after Friday prayers in downtown Amman Feb. 6, 2015. Reuters/Muhammad Hamed

Jordanian fighter jets completed a third round of bombing against the Islamic State group Saturday in retaliation for the burning death of a pilot who had been taken hostage. The offensive came after the extremist group claimed without proof that American Kayla Mueller was killed during Jordanian airstrikes conducted in recent days.

The militant group formerly known as either ISIL or ISIS released a gruesome video Tuesday depicting Jordanian pilot Lt. Muath al-Kaseasbeh, who was captured in Syria in December, being burned alive in a cage. Jordan launched what it promised would be an “earthshaking” response Thursday, with airstrikes aimed at the city of Raqqa and elsewhere in Syria.

“Sorties of air fighters today bombed bases of the [Islamic State] terror gang,” Jordanian state media said in a news bulletin Saturday, according to Reuters.

Jordan has not been acting alone. The country has been an integral part of the U.S.-led coalition targeting the Islamic State group in Iraq and Syria, but since the death of al-Kaseasbeh it has also carried out retalatory strikes on its own.

A representative of the Combined Joint Task Force-Operation Inherent Resolve told International Business Times that “strikes on 06 February 2015 followed the coalition’s standard selection and approval process. The strike missions, along with the approproate coalition support sorties, were planned and executed within the normal air tasking order cycle.”

“This is the beginning,” said an Arabic-language statement released by the Jordanian government, as it promised to further “the killing of evil where it hides ... in response to the criminal, cowardly act ... that was carried out by a treacherous and tyrannical gang against the body of our pure martyr.”

Jordan’s King Abdullah II called for increased cooperation between Muslims and Christians in the fight against terrorism.

The U.S. government has said it is still investigating the Islamic State group’s claim that Mueller, an American aid worker believed to have been taken captive last year, was killed in the fighting.

The surge in tension between Jordan and the Islamic State group has been enough to convince the American military to move search-and-rescue aircraft closer to the fighting, in the hope that similarly brutal deaths might be avoided in the future. The U.S.-led coalition has also continued bombing specific targets along the border that separates Iraq and Syria.

Alessandria Masi contributed reporting to this story.