AMMAN, Jordan -- Islamic State militants put to death a captured Jordanian fighter pilot by burning him alive in a cage, according to a video the group released Tuesday. The kingdom vowed a swift and lethal response to what it called a "barbaric" act.

The military confirmed the death of Lt. Muath Al-Kaseasbeh, who was captured by the extremists in December when his F-16 crashed while he was flying a mission as part of the U.S.-led air campaign against the Islamic State.

Jordanian TV said the pilot was killed as long ago as Jan. 3. In the past week, the militants had not responded to demands by Jordanian authorities to deliver proof the airman was alive so a prisoner swap could be made.

The killing of the 26-year-old pilot appeared aimed at pressuring the government of Jordan -- a close U.S. ally -- to leave the coalition that has carried out months of airstrikes targeting Islamic State positions in Syria and Iraq. But the extremists' brutality against a fellow Muslim could backfire and galvanize other Sunni Muslims in the region against them.

King Abdullah II, who has portrayed the campaign against the extremists as a battle over values, was in Washington on a previously scheduled trip. He added a stop at the White House with President Barack Obama. The monarch broadcast a speech on Jordanian TV on Tuesday evening, confirming the pilot's death "with sorrow and anger," and urging his countrymen to unite.

"It's the duty of all of us to stand united and show the real values of Jordanians in the face of these hardships," Abdullah said. The official Petra news agency said he would be cutting short his Washington trip.

Obama said the Islamic State group's video, if authentic, showed "the viciousness and barbarity of this organization."

"And it, I think, will redouble the vigilance and determination on the part of a global coalition to make sure that they are degraded and ultimately defeated," he told reporters during an event at the White House.

Obama later issued a statement offering condolences, saying the pilot's "dedication, courage, and service to his country and family represent universal human values that stand in opposition to the cowardice and depravity of ISIL, which has been so broadly rejected around the globe." The Islamic State group is known variously by the acronyms ISIL, ISIS and, in Arabic, Daesh.

Dozens of people chanting slogans against the Islamic State marched toward the royal palace to express their anger. Waving a Jordanian flag, they chanted, "Damn you, Daesh!" and "We will avenge, we will avenge our son's blood."

Jordanian officials said the country would response swiftly and decisively.

"Our punishment and revenge will be as huge as the loss of the Jordanians," said the spokesman of the armed forces, Mamdouh al-Ameri.

One option is to move forward with the execution of Sajida al-Rishawi, an al Qaeda prisoner whom Jordan had offered to trade for the pilot.

Al-Rishawi, 44, faces death by hanging for her role in the bombings of three Amman hotels in 2005. Al-Rishawi's suicide belt did not detonate at the time and she fled the scene, but was quickly arrested. After a televised confession, she recanted, but her appeal was turned down.

Al-Rishawi, an Iraqi national, has close family ties to the Iraqi branch of al Qaeda, a precursor of the Islamic State group.

The 20-minute video purportedly showing the pilot's killing was released on militant websites and bore the logo of the extremist group's al-Furqan media service. The clip featured the slick production and graphics used in previous Islamic State videos.

The pilot showed signs of having been beaten, including a black eye. Toward the end of the video, he was shown wearing an orange jumpsuit. He stood in an outdoor cage as a masked militant ignited a line of fuel leading to it.

The video, which could not immediately be confirmed independently by The Associated Press, threatened other purported Jordanian pilots by name.

It emerged three days after Japanese journalist Kenji Goto was purportedly beheaded by the militants. The fate of the journalist and the pilot had been linked by their captors.

Al-Kaseasbeh is from a tribal area in southern Jordan's Karak district. The tribes are considered a mainstay of support for the monarchy, but the pilot's capture has strained that relationship. Members of the pilot's family have repeatedly accused the government of botching efforts to win his release and have also criticized Jordan's participation in the anti-IS alliance.

The pilot's father, Safi Yousef al-Kaseasbeh, was attending a tribal meeting in Amman when news of the video surfaced, and he was seen being led from the session. Other men were seen outside, overcome with emotion.

Late Tuesday, as word spread of his death, protesters marched in his home village of Ai and set a local government office on fire. Witnesses said the atmosphere was tense and that riot police were patrolling the streets.

In Amman, family members gathering at a tribal meeting place wept when receiving word of his death. Outside, hundreds of protesters took to the streets, chanting: "There is no god but God and the martyr is beloved by God."

Al-Kaseasbeh had fallen into the hands of the militants in December when his F-16 crashed near Raqqa, Syria, the de facto capital of the group's self-styled caliphate. He is the only coalition pilot to be captured to date.

The Islamic State group, which controls around a third of Syria and neighbouring Iraq, has released a series of gruesome videos showing the killing of captives, including two American journalists, an American aid worker and two British aid workers. Tuesday's was the first to show a captive being burned alive.

Members of the UN Security Council condemned the killing of the pilot. Sauomg ot demonstrated "the brutality of ISIL, which is responsible for thousands of crimes and abuses against people from all faiths, ethnicities and nationalities, and without regard to any basic value of humanity."

David L. Phillips, a former State Department adviser on the Middle East, said he believes the pilot's killing could backfire, antagonizing Sunnis against the extremists, including Sunni tribes in Iraq.

"They need to have a welcome from Sunni Arabs in Anbar Province (in Iraq) to maintain their operations," said Phillips, director of the Program on Peace-building and Human Rights at Columbia University.

He said the extremist group's recent military setbacks may have fueled the killings. "They need to compensate for that with increasingly gruesome killings of prisoners," he said.

Jordan has made clear that the hostage crisis will not prompt it to leave the coalition.

"We now all know in Jordan, beyond any doubt, how barbaric ISIS is," said Mohammed al-Momani, a government spokesman. "Whoever doubted the unity of Jordan will now be proved wrong. Whoever doubts Jordan's stern and lethal response will be proved wrong."

Experts are divided over whether Jordan faces a greater threat from extremists outside its borders or from those within. In recent months, there have been signs of greater support for the Islamic State group's ideas among Jordan's young and poor. Last year, the government intensified a crackdown on IS sympathizers and the al Qaeda branch in Syria.