WASHINGTON — Dozens of Americans have traveled or tried to travel to Syria to fight with the rebels against the government of President Bashar al-Assad since 2011, American intelligence officials said Wednesday.

The Americans are a small subset of the mostly radicalized young Muslims with Western passports who are entering Syria from Europe, North America and Australia, a group that numbers roughly 600, according to the officials and classified estimates from Western spy agencies. That represents a fraction of the roughly 6,000 to 11,000 foreign fighters over all who have poured into Syria by way of the Middle East and North Africa.

The Americans’ numbers are small — intelligence officials would not be more precise than saying “dozens” were involved — and they have so far not distinguished themselves on the battlefield. But they are part of what officials said was a growing presence of foreigners who are fighting Mr. Assad’s government.

“It’s a very steady increase, and I expect that to continue as long as the fighting there continues,” a senior American intelligence official said.