Updated

U.S. officials have intercepted intelligence indicating Iran recently urged militants to strike the U.S. embassy in Baghdad -- raising the possibility that the country is looking to orchestrate revenge attacks if the United States launches missiles at its ally Syria.

The Wall Street Journal first reported that the U.S. had intercepted an order from Iran to militants in Iraq, telling them to attack if there is a Syria strike.

A senior military source told Fox News that there is indeed such an intelligence intercept, but the intelligence has not been completely vetted.

Still, a separate senior U.S. official said it's quite common for Iran to be giving orders to hit the embassy in Baghdad. When rockets hit the compound, the orders are often traced back to elements in Iran.

This official said he was not aware of any increased security at the Baghdad embassy, or any reductions in embassy staff, as a protective measure. The Baghdad embassy remains the largest, most heavily fortified embassy in the world.

Amid the heightened tensions, though, the U.S. is taking other precautionary measures. The warnings and precautions underscore the risk the U.S. could be taking by launching a military hit on a Middle East country embroiled in civil war.

The State Department on Friday ordered nonessential American diplomats and the families of staffers at the U.S. Embassy in Beirut to leave Lebanon immediately due to security concerns as Congress debates whether to authorize an attack on Syria. The department also authorized the voluntary departure of diplomats and families at the U.S. Consulate in Adana, Turkey, which is the closest American diplomatic post to Syria in Turkey.

In a new travel warning for Lebanon, the department said it had instructed nonessential staffers to leave Beirut and urged private American citizens to depart the country "due to threats to U.S. mission facilities and personnel."

"The potential in Lebanon for a spontaneous upsurge in violence remains," it said.

The step had been under consideration since last week when Obama said he was contemplating military action against the Syrian government for its alleged chemical weapons attack last month that the administration said killed more than 1,400 people near Damascus.

Hezbollah, an Assad ally that has sent fighters into Syria, is based in Lebanon and the department noted that Hezbollah "maintains a strong presence in parts of the southern suburbs of Beirut, portions of the Bekaa Valley and areas in South Lebanon."

The Journal report also quoted U.S. officials saying they fear Hezbollah could attack the U.S. embassy in Beirut.

The message purportedly from Iran was intercepted recently, according to the Journal, and came from the head of the Revolutionary Guards' Quds Force. It reportedly went to Shiite militia groups in Iraq.

Click for more from The Wall Street Journal.

Fox News' Jennifer Griffin and Justin Fishel and The Associated Press contributed to this report.