LONDON — Following an emergency meeting on Sunday with Britain’s top security and military officials to form a response to the beheading of a British aid worker by the Islamic State in Iraq and Syria, Prime Minister David Cameron laid out a plan to support American military action in those two countries but made no commitment to a more vigorous military role.

“This is not about British combat troops on the ground,” Mr. Cameron said. “It is about working with others to extinguish this terrorist threat.” He said British Tornadoes and surveillance aircraft had been helping with logistics and intelligence-gathering in the region.

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.

The execution of the aid worker, David Cawthorne Haines, was announced by the Islamic State in Iraq and Syria, or ISIS, in a video released Saturday night. It was a clear message to Britain, a vital ally of the United States as it builds an international coalition to target ISIS. The militant group has made major advances across Syria and northern Iraq in recent months.