Jordan said Thursday it had launched air strikes against the Islamic State group, after vowing a harsh response to the burning alive of one of its fighter pilots.

"The Jordanian air force launched raids against positions of the Islamic State group," said a government official, who did not want to be named.

He did not disclose where the strikes took place, saying the military would release a statement on the operation later.

Jordan has conducted regular raids against IS in Syria as part of a US-led campaign against IS, which has seized swathes of the country and of neighboring Iraq.

The gruesome murder of airman Maaz al-Kassasbeh, who was captured by IS when his F-16 fighter plane went down in Syria in December, has boosted support in Jordan for increased military action against the jihadists.

Jordanian King Abdullah II personally paid his condolences Thursday to the pilot's family in his hometown of Karak, 120 kilometres (74 miles) south of the capital.

Abdullah cut short a visit to the United States and flew back to Amman on Wednesday after the harrowing video emerged of Kassasbeh's killing.

"The blood of martyr Maaz al-Kassasbeh will not be in vain and the response of Jordan and its army after what happened to our dear son will be severe," he said afterwards.

On Wednesday, Jordan executed two Iraqis on death row -- female would-be suicide bomber Sajida al-Rishawi and Al-Qaeda operative Ziad al-Karboli -- in response to the killing of the 26-year-old pilot.