A video released by Islamic State Friday purports to show the execution of British citizen Alan Henning, who was kidnapped while delivering aid in Syria.

LONDON—U.K. Prime Minister David Cameron said Britain will do all it can to hunt down those responsible for the killing of Alan Henning, after a video appearing to show the British aid worker’s beheading was released by Islamic State militants late Friday.

The video surfaced days after Britain’s Parliament authorized military action against Islamic State, followed by the Royal Air Force’s participation in the U.S.-led fight against the extremist group.

British officials said Saturday they are also examining a second video featuring an unmasked—apparently British—Islamic State fighter delivering a message.

“The police are urgently investigating the contents of the video, including possible terrorism offences relating to it,” a spokesman said, without giving further details.

Mr. Cameron, who had just returned from a trip to Afghanistan to meet the country’s new president, received a briefing Saturday morning about the video of Mr. Henning from officials at U.K. intelligence agencies, the armed forces and the Foreign Office.

“The murder of Alan Henning is absolutely abhorrent,” said Mr. Cameron after the briefing in an interview with British Broadcasting Corp. Mr. Henning was “a man of great peace, kindness and gentleness,” said the prime minister, speaking from his official country residence, Chequers.

Mr. Henning left his job in the U.K. as a taxi driver to drive in a convoy to Syria to help deliver aid, including diapers and baby formula, to refugees. He was taken prisoner in December. His apparent killing marks the fourth beheading of a Western hostage by the jihadist group, beginning with the killing of American journalist James Foley in August.

British Prime Minister David Cameron speaks during a news conference in Kabul on Friday. Mr. Cameron on Saturday called the killing of aid worker Alan Henning "abhorrent." Reuters

Referring to Islamic State, Mr. Cameron said, “Anybody in any doubt about this organization can now see how truly repulsive it is and barbaric it is.”

Mr. Cameron said that the U.K., in cooperation with its allies, will continue to use all the assets it has to combat the militants overseas and at home. “We will do everything we can to find and hunt down the people responsible for this,” Mr. Cameron said.

Asked whether the U.K. and its allies could stop the same thing happening again to other hostages, Mr. Cameron said, “What we see with this organization is that there is no level of depravity to which they won’t sink.”

At least one other British hostage has featured in a video released by Islamic State, who appears to be British photojournalist John Cantlie. The Foreign Office declined to comment on the hostage.

“As a family we are devastated by the news of his death. There are few words to describe how we feel at this moment,” read a statement issued by Mr. Henning’s family. “He will be remembered for this and we as a family are extremely proud of him and what he achieved and the people he helped.”

The United Nations Security Council late Friday called the killing of Mr. Henning “heinous and cowardly,” reiterating that Islamic State “must be defeated and that the intolerance, violence and hatred it espouses must be stamped out.”

—Jason Douglas contributed to this article.

Write to Cassell Bryan-Low at cassell.bryan-low@wsj.com and Jenny Gross at jenny.gross@wsj.com