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The Islamic State in Iraq and Syria released a video Saturday of the third beheading of a foreign hostage, a British aid worker, according to SITE Intelligence, which tracks the jihadist groups. The killing was a clear message to Britain, a vital ally of the United States as it builds an international coalition to target the militant group, which has made stunning advances across Syria and northern Iraq in recent months.

The video shows the aid worker, David Cawthorne Haines, kneeling on a bare hill under the open sky, in a landscape that appears identical to where two American journalists were killed by the group in back-to-back-executions in the past month. In the moments before his death, the 44-year-old Mr. Haines is forced to read a script, in which he blames his country’s leaders for his killing.

“I would like to declare that I hold you, David Cameron, entirely responsible for my execution,” he said. “You entered voluntarily into a coalition with the United States against the Islamic State.” He added: “Unfortunately, it is we the British public that in the end will pay the price for our Parliament’s selfish decisions.”

The video ends with the black-clad executioner identifying their next victim as Alan Henning, another British citizen.

The beheading of Mr. Haines puts pressure on the government of Prime Minister Cameron of Britain, a member of a “core coalition” of nations announced as NATO leaders met in Wales this month and sought to devise a strategy to address the growing threat from ISIS, including plans to strengthen allies in Iraq and Syria and conduct airstrikes against the militants.

President Obama last week announced a major expansion of the military campaign against ISIS, including airstrikes against the group in Syria. The beheadings of the two Americans, James Foley reported on Aug. 19 and Steven J. Sotloff on Sept. 2, followed the start of a campaign of airstrikes against ISIS positions in Iraq.

The group is currently holding Mr. Henning and another British citizen, as well as two other American aid workers. Their families have asked the news media not to disclose their names, after ISIS warned that the hostages would die if relatives made their identities public.

The British government said it was trying to verify the video. Mr. Cameron later denounced the killing on Twitter: “The murder of David Haines is an act of pure evil. My heart goes out to his family who have shown extraordinary courage and fortitude.”

“We will do everything in our power to hunt down these murderers and ensure they face justice, however long it takes.”

Britain and the United States are among the only nations in the world that have held to a hard-line, no-concessions policy when dealing with kidnappings by terrorist groups.

Until earlier this year, ISIS was holding close to two dozen foreigners in the same jail where Mr. Haines was imprisoned, on the outskirts of the Syrian town of Raqqa. His European cellmates were released for ransom, one after another, according to one of the hostages held alongside him who was recently freed after his government paid a ransom. Mr. Haines, who had a military background, was kidnapped 19 months ago in northern Syria and was held alongside an Italian co-worker, Frederico Motka.

Both men worked for Acted, a French aid group, and had traveled to Syria to try to help during the country’s horrific civil war. Their fates diverged based on their countries’ policies: Mr. Motka was released in May, one of 15 Europeans who were released from the same ISIS-run jail for a ransom, according to a person familiar with the hostages’ detention and release.

Earlier this month, Mr. Cameron ruled out paying a ransom for Mr. Haines. “It’s a desperately difficult situation,” he told Sky News. “We don’t pay ransoms to terrorists when they kidnap our citizens.”

The British news media respected a strict blackout, not revealing that Mr. Haines, a father of two from Perth, Scotland, was missing until the video of Mr. Sotloff’s execution was released on Sept. 2, That video named Mr. Haines as the next to be killed.

Mr. Haines had been working as a security consultant for Acted when he was captured in a refugee camp in Atmeh, in northern Syria. On his LinkedIn profile, he wrote that he had 23 years of “working experience in private, NGO and military environments,” referring to nongovernmental organizations. Before Acted, Mr. Haines worked in South Sudan in 2012 for a Belgium-based organization, Nonviolent Peaceforce, which describes itself as an “unarmed, civilian peacekeeping force” and operates in South Sudan, Myanmar and the Philippines.

He also worked as a country director for Handicap International, a disability charity, in Libya during the Arab Spring.

During his captivity, he tried to hide his military background, a former hostage said, but like many of the others held in a cell in Raqqa, he was repeatedly tortured, one of his former cellmates said.

In the video, his executioner, speaking English with a British accent, makes reference to Mr. Haines’s background, indicating that they eventually found out: “This British man has to pay the price for your promise to Cameron to arm the pesh merga against the Islamic State. Ironically, he has spent a decade of his life serving under the same Royal Air Force that is responsible for delivering those arms.”

Mr. Haines also held various positions in the military, according to his profile on social media sites, describing them as “covering security and threat assessments” in a number of countries.

On Friday, Mr. Haines’s family issued a brief statement to the militants appealing with them to make contact. “We are the family of David Haines,” said the statement, which was released by Britain’s Foreign and Commonwealth Office. “We have sent messages to you to which we have not received a reply. We are asking those holding David to make contact with us.”

The BBC reported that imams across Scotland, where Mr. Haines’s parents live, called for the release of Mr. Haines and other hostages during Friday Prayer last week.

Rukmini Callimachi reported from New York, and Kimiko de Freytas-Tamura from London.