REUTERS/Thaier al-Sudani
Fighters from Iraq's Islamist Shi'ite militias celebrate before departing to
The American embassy in Baghdad was a likely target, according to unnamed U.S. officials quoted by the newspaper. The Journal said the officials did not describe the range of potential targets indicated by the intelligence.
In addition, the State Department issued a warning on Thursday telling U.S. citizens to avoid all but "essential" travel to Iraq.
President Barack Obama has asked the U.S. Congress to back his plan for limited strikes in response to a chemical weapons attack on civilians that the United States blames on Syrian President Bashar al-Assad's forces.
The Journal reported that the Iranian message was intercepted in recent days and came from the head of the Revolutionary Guards' Qods Force. The newspaper said the message went to Iranian-supported Shi'ite militia groups in Iraq.
The Journal reported that the message informed Shi'ite groups to be prepared to respond with force after any U.S. military strike on Syria.
"Travel within Iraq remains dangerous given the security situation," according to the State Department's warning, which replaced an earlier one "to update information on security incidents and to remind U.S. citizens of ongoing security concerns in Iraq, including kidnapping and terrorist violence."
The department said that numerous insurgent groups, including al Qaeda's Iraq affiliate, remain active and "terrorist activity and sectarian violence persist in many areas of the country at levels unseen since 2008."
It added: "The ability of the embassy to respond to situations in which U.S. citizens face difficulty, including arrests, is extremely limited."
The State Department declined immediate comment. The CIA declined comment.
(Additional reporting by Tabassum Zakaria; Reporting by Will Dunham and Arshad Mohammed; Editing by Eric Walsh)