“I knew this war will be long,” he said. “Requires steadfastness.”

Both men said they were appalled by the West’s failure to halt the killing in Syria. They are also united in a wider goal, they said, to establish a caliphate ruled by Shariah law, even if that ideology is not shared by a majority of Muslims in Syria.

A total of 11,000 foreign fighters are estimated to be in Syria, including those from other Muslim nations as well as those from the West, said researchers at the Center for the Study of Radicalization and Political Violence.

The British and the French are thought to make up the largest contingent of Westerners — 400 and 700 — among the fighters, according to government estimates. Several hundred Belgians, Dutch and Scandinavians are also thought to be fighting, according to official figures. A minority of fighters are from Eastern Europe, including Albania, Bosnia and Serbia, and also from Australia and Canada, according to the center. The estimate of 70 from the United States is up from about a dozen last July.

Most Westerners who go to Syria go to wage jihad, but even those who go for purely humanitarian reasons end up being radicalized, Mr. Van Ostaeyen said.

One of the most popular — and extreme — of the fighting groups among Westerners in Syria calls itself the Islamic State of Iraq and Syria, or ISIS. Part of its appeal comes from its extensive public outreach, experts say. The group is the most prolific on social media compared with other groups — it has several official Twitter accounts and its own media channels. Its fighters habitually post on Twitter about their activities in English and other Western languages, and even argue for days with other Twitter users who oppose the group’s ideology.

Many fighters share the belief that Islam is under attack by non-Muslims — a view they say is expressed in the Quran and popularized by the Qaeda leader Osama bin Laden.

On Sept. 11, 2001, Abu Sumayyah and Abu Muhajir were teenagers interested in video games, sports and the start of college. But both men said they were deeply affected by the subsequent invasion of Afghanistan and Iraq and the American drone strikes in Pakistan and Yemen. They came to question the Western world they lived in, and their role in it.