Jordan's King Abdullah II vowed Wednesday that his military forces would hit Islamic State militants with "relentless" strikes upon "their own homes," an escalation that could place Jordan in the middle of the Syrian civil war.

The king huddled with his security cabinet and top generals Wednesday just hours after Jordan hanged two convicted terrorists in retaliation against the Islamic State, which posted a video Tuesday of its fighters burning alive a captured Jordanian pilot in a cage.

The immolation prompted harsh condemnation from leaders across the Middle East and in the United States, with the White House speaking of Jordan's "strength and commitment" to the international coalition against the Islamic State "in the face of this barbaric act."

In Jordan, the killing mostly silenced critics of the U.S.-led offensive against the Islamic State, the heavily armed al-Qaida offshoot also known as ISIS or ISIL. It was used by the government to stoke patriotic sentiment, with billboard-size posters in Amman reading "We Are All Jordan" and a rally of flag-waving supporters greeting the king at the airport as he arrived back in the country.

"We will be on the lookout for these criminals, and we will hit them in their own homes," Abdullah declared, according to the state news agency Petra. "We are fighting this war to protect our faith, values and our humanitarian principles. Our fight will be relentless."

The hangings underscored the hardening stance by the monarch and his military in Jordan, a key U.S. ally in the fight against the Islamic State, amid street protests calling for revenge against the militant group.

The backlash from the video -- released while Abdullah was in Washington to sign a deal boosting the amount of U.S. aid to Jordan -- appears to have drawn the usually cautious monarch into a direct confrontation with radical Islamists.

The king, who claims to be a descendant of the prophet Muhammad and was educated in Britain and the United States, has previously avoided direct threats against the Islamic State and has sought to keep secret the number of bombing missions his air force has flown over Syria.

But according to Rep. Duncan Hunter, R-Calif., Abdullah -- who met with members of Congress before he left Washington -- quoted the Clint Eastwood character William Munny, an aging gunslinger in the Oscar-winning film "Unforgiven" who exacts vengeance when his friend is tortured to death.

Abdullah did not elaborate on where or how Jordan's retaliation would be carried out.

It is unlikely that Jordan would fly strike missions in Syria outside those coordinated by the U.S-directed coalition. Out of nearly 1,000 strikes in Syria since September, the vast majority have been by U.S. aircraft. But "the coalition is not going to turn their nose up at additional kinetic activity by one of the members," said a senior U.S. defense official in Washington. "If they want to do more, we welcome it."

Overall, the coalition strategy and the pattern of strikes will not change, said the official, who was not authorized to discuss the matter and spoke on the condition of anonymity. But outside of coalition operations, "we can't speak for Jordan," the official said. "They might feel that for their own sense of national pride, they need to do something."

The Obama administration declined to join with the European Union -- where there is no death penalty -- in criticizing the rapid Jordanian executions. White House press secretary Josh Earnest noted that both individuals "had gone through the Jordanian justice system" and were "sentenced to death."

The administration did not immediately respond to a letter sent to Defense Secretary Chuck Hagel and Secretary of State John Kerry from the Senate Foreign Relations Committee, which wrote that Abdullah, in a meeting with them in Washington before his departure for Amman on Tuesday, had complained of "complications and delays" in providing defense items such as aircraft parts and munitions.

Jordan's chief government spokesman said the two prisoners executed Wednesday included Sajida al-Rishawi, an Iraqi woman sentenced to death for her role in a deadly 2005 terrorist attack in Amman. The Islamic State had sought her release as part of a possible prisoner swap. Jordan had offered to free Rishawi in exchange for the pilot, Lt. Muath al-Kaseasbeh, and a Japanese journalist, Kenji Goto, held by the Islamic State.

The other inmate was Ziad al-Karbouli, who was linked to a terrorist attack against Jordanians in Iraq in 2005 and whose freedom was also demanded by the Islamic State.

The two were hanged less than 12 hours after the video of the pilot's killing was posted online.

Across Jordan, voices that recently called for the country to withdraw from the U.S.-led offensive against the Islamic State fell silent as Jordanians came together to denounce the militants.

"This terrible act has created tremendous unity in Jordan," said Jawad Anani, a senator and former foreign minister. "Ordinary Jordanians now see the threat to their own security."

Anani, who is close to Abdullah, suggested that airstrikes by Jordan and the coalition would intensify, and he said it was possible that Jordanian ground troops or special forces might be deployed in Syria.

"The next logical step, you can intensify the conflict," Anani said.

But others doubt that the backlash will stir major changes in Muslim participation in the U.S.-led coalition against the Islamic State in Syria and Iraq.

"The killing's impact on the coalition will not really be a game-changer, because the participation of countries depends on a variety of issues that are specific to each country," said Elias Hanna, a retired Lebanese general who teaches geopolitics at the American University of Beirut.

"We won't see Arab boots on the ground," he predicted. "That's for certain."

In his first public statement since the video, Safi al-Kaseasbeh, the pilot's father, said Wednesday that he expects Jordan and the U.S.-led coalition to avenge his son's death. Just last week, the elder Kaseasbeh had appealed for Jordan to pull out of the coalition.

"I urge the government, I expect the government, to seek revenge, severe revenge, for the blood of Muath against this horrid organization, this criminal organization, this organization that is far from Islam and the spirit of Islam," the pilot's father said Wednesday.

Members of the extended Kaseasbeh clan greeted a stream of visitors at their mourning tent outside the city of Karak, south of Amman. The family had no body to bury. On the video, Islamic State fighters are shown dumping a bulldozer load of cement rubble over his body.

Mosques across Jordan held prayers for Kaseasbeh at noon, with government-supported imams denouncing the Islamic State. Meanwhile, Christian churches in Amman pealed their bells in interfaith solidarity. After noon prayers, Royal Jordanian Air Force fighter jets flew over Amman and Karak.

But Jordan also faces tests on whether it can build on the displays of unity and resolve. There have been past signs of support for the Islamic State in Jordan -- especially in poorer regions -- although relatively few have waved Islamic State flags or endorsed the group on the Internet.

Labib Kamhawi, an Amman-based political analyst, said Abdullah is in "a difficult position" on how to frame the response.

"The issue is whether he can transform this into a national issue that affects Jordanians, or whether it becomes a tribal matter with mounting calls for revenge and eye-for-an-eye attacks," he said.