BAGHDAD (AP) — Angered by deadly airstrikes targeting an Iran-backed militia, dozens of Iraqi Shiite militiamen and their supporters broke into the U.S. Embassy compound in Baghdad on Tuesday, smashing a main door and setting fire to a reception area in one of the worst attacks on the embassy in recent memory.

American guards fired tear gas, and palls of smoke rose over the embassy grounds.

An Associated Press reporter at the scene saw flames rising from inside the compound and U.S. soldiers on the roof of the main embassy building with their guns pointed at protesters.

A man on a loudspeaker...