"We're definitely at a high state of vigilance," the official said in confirming a CNN report that said an attack could come in the next week.
Suspected Israeli warplanes bombed Iran's embassy in Damascus on Monday in a strike that killed an Iranian military commander and marked a major escalation in Israel's war with its regional adversaries.
Iran's Islamic Revolutionary Guard Corps has said that seven Iranian military advisers died in the strike, including Mohammad Reza Zahedi, a senior commander in its Quds Force, which is an elite foreign espionage and paramilitary arm.
Does Iran have a right to respond?
Iran has said it reserves the right "to take a decisive response."
US President Joe Biden discussed the threat from Iran in a phone call on Thursday with Israeli Prime Minister Benjamin Netanyahu.
"Our teams have been in regular and continuous contact since then. The United States fully supports the defense of Israel against threats from Iran," a senior Biden administration official said.