Jordan retaliated Thursday with F-16 airstrikes on the Syrian town of Raqqa and is vowing a relentless war against the Islamic State, also known as ISIL and ISIS. Members of Congress are calling on the White House to approve a list of weapons for King Abdullah II, a strong U.S. ally.

Rep. Duncan Hunter, California Republican, sent a letter Thursday asking President Obama to approve the transfer of the Predator’s unarmed export version for surveillance missions. “The decision to deny the license request should be reversed immediately,” Mr. Hunter wrote. “Doing so will provide Jordan critical mission capability in the fight against the Islamic State and ensure Jordan is given every advantage. Jordan has made requests for specific resources, including ammunition,” Mr. Hunter said. “Given our mutual interests, and our strong relationship, it’s absolutely critical that we provide Jordan the support needed to defeat the Islamic State.”

Jordan borders Iraq and Syria, where the Islamic State controls wide stretches of territory, including key Iraqi cities in the north and west. “Jordan is uniquely positioned to support and perhaps lead the fight against the Islamic State, and it’s now our obligation to offer Jordan our full support in this effort,” Mr. Hunter said. American Predators are playing a large role in a U.S.-dominated air campaign, firing Hellfire missiles as well as conducting sustained surveillance over Islamic State strongholds.

Jordan is not the only world hot spot where the Obama administration has turned down allies’ requests for weapons. For months, Ukraine has been seeking military assistance from the U.S. and/or NATO in its battles against pro-Russia separatists getting lethal weaponry and even some troops from Vladimir Putin’s Russia. Ukraine’s military is equipped mostly with Russian weapons inherited from the breakup of the Soviet Union, with some purchases from Moscow in friendlier recent times. But the U.S. has refused to provide lethal aid to Ukraine, sending only humanitarian assistance amounting to tens of millions of dollars and, for the Ukrainian military, a similar amount of training and nonlethal equipment such as trucks.

Ukrainian President Petro Poroshenko told U.S. lawmakers in September that his country was in desperate need. “Please understand me: Blankets and night vision goggles are also important, but one cannot win the war with blankets,” he told a joint meeting of Congress. Secretary of State John F. Kerry was in Ukraine Thursday, where he was set to announce a $16 million package in civilian refugee aid that will include blankets and counseling for traumatized civilians.

A congressional aide said Jordan does not quality for armed Predators but could be given the limited platform. The source said the administration’s denial has to do with making sure Israel maintains military superiority in the region. Jordan was the second Arab state to sign a peace treaty with Israel, in 1994, a pact that is not considered precarious barring drastic regime change in Jordan. The U.S. has provided Jordan with F-16 Falcon fighter jets and other advanced weapons.

Mr. Hunter’s district is in the San Diego area, home to Predator maker General Atomics.

Sen. John McCain, Arizona Republican and Senate Armed Services Committee chairman, told CNN on Wednesday that King Abdullah, who met with senators while in Washington, is frustrated by a “huge bureaucratic bottleneck in the State Department.”  “He needs some types of weapons very badly,” Mr. McCain said. “We’ll be working immediately to try and achieve that for him.”  The issue of Jordanian frustration with the speed of U.S. weapons deliveries came up during Wednesday’s confirmation hearings for Defense Secretary-designate Ashton Carter. All 26 members of Mr. McCain’s committee sent a letter on Wednesday to Defense Secretary Chuck Hagel and to Mr. Kerry asking them to speed up arms shipments to Jordan.

“Jordan is seeking to obtain aircraft parts, additional night vision equipment and precision munitions that the King feels he needs to secure his border and robustly execute combat air missions into Syria,” the senators wrote. “We understand the need to ensure the integrity of third party transfers, the protection of critical U.S. technologies, and our commitment to the maintenance of a Qualitative Military Edge (QME) for Israel. However,” the senate panel continued, “Jordan’s situation and the cohesiveness of the coalition demands we move with speed to ensure they receive the military materiel they require for ongoing operations against ISIL.”

Jordan’s King Abdullah II has vowed to launch war on the Islamic State, saying Wednesday that “the blood of martyr [Lt.] Muath al-Kaseasbeh will not be in vain, and the response of Jordan and its army after what happened to our dear son will be severe.”  On Thursday, dozens of Jordanian F-16s carried out strikes on targets around Raqqa, the Islamic State’s self-styled capital, and even spread its attacks into Islamic State-held targets in Iraq. Foreign Minister Nasser Judeh told Fox News that Jordan was still mostly hitting Islamic State targets in Syria as part of a U.S.-led military coalition, but was now spreading its involvement.

“We said we are going to take this all the way, we are going to go after [the Islamic State] wherever they are, and we’re doing that,” he said. “They’re in Iraq and they are in Syria, and therefore you have to target them wherever they are.”

According to The Associated Press in Amman, Jordanian state TV showed fighter jets taking off from an air base and large balls of fire and smoke after bombs had fallen. Jordanian troops scribbled chalk messages on the missiles, with one reading “for you, the enemies of Islam.” Abdullah paid a condolence visit to the family of Lt. al-Kaseasbeh on Thursday and was sitting next to the pilot’s father, Safi al-Kaseasbeh, as fighter jets roared overhead. The king pointed upward.

The official Facebook page of The Royal Hashemite Court made it personal as well this week. In an image that has since gone viral, the Court posted a picture of Abdullah in military fatigues, and noted that he’d cut short his U.S. visit in response to the pilot’s death. According to Mr. Hunter, Abdullah quoted a line from Clint Eastwood’s revenge Western “Unforgiven” at a meeting with U.S. Congress members Tuesday after the news of the burning death had broken.

While the Jordanian government has denied Abdullah would take part in actual attacks, he has been called the “warrior king” due to his decades of military service. Like his father and predecessor, King Hussein, Abdullah enrolled in the U.K.’s Royal Military Academy at Sandhurst. The current king has been a pilot for Cobra attack helicopters.

For its part, the Islamic State has signaled that its fire execution will not be its last, according to translations of its official Twitter account by the Middle East Media Research Institute. After Jordanian Air Force Lt. Muath al-Kaseasbeh was set on fire while caged, the Islamic State’s “Fatwa and Research Authority” called such burnings “completely permissible” under Muslim law in a series of theological discussions and accounts of Muslim history and scholarship, including the actions of Muhammad. According to MEMRI, the Islamic State deemed Lt. al-Kaseasbeh a non-Muslim or apostate, and noted that Muslim schools of jurisprudence have interpreted loosely the apparent Koranic prohibition on “burning an infidel with fire until he dies.” “The Hanafi and Shafi’i schools hold that burning is completely permissible. They interpreted the saying of the Prophet that ‘Only Allah shall torture with fire’ as [a call for] humility. [The scholar] Al-Muhallab said: ‘This ban is not [an actual] prohibition, but rather a means for [advocating] humility.’ [Shafi’i scholar] Ibn Hajar, may Allah have mercy on him, said: ‘[This saying] indicates that it is permissible to burn, as the Companions did. The Prophet blinded two men from ‘Arina [whom he judged to be apostates and criminals] with a branding iron. Khalid bin Al-Walid, [one of the Prophet’s Companions], also burned apostates with fire.'”

• Douglas Ernst contributed to this article, which is based in part on wire service reports from the Middle East.  © Copyright 2015 The Washington Times, LLC.