A gunbattle between militants and security forces in the area was still going in early morning.
Sayed Fazlullah Wahidi, the governor of Herat province, says it's unclear if any of the militants managed to get inside the compound.
No group claimed responsibility for the attack, but Taliban insurgents have often used combined car bomb and gun assaults against various targets in Afghanistan.
A US Embassy spokesman in Kabul declined immediate comment.
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