"There is a good level of coordination with Iran on this issue and I cannot reveal more. But I can say that there will be a strong response," he told The Associated Press. "Each armed group will have duties to carry out."
Al-Batat was a senior official in Iraq's Hezbollah Brigades, which is believed to be funded and trained by Iran's Revolutionary Guard.
He rose to greater prominence earlier this year when the group he claims to lead issued threats against Sunni residents in parts of Baghdad. He later claimed responsibility for deadly rocket attacks on a Baghdad-area camp housing Iranian dissidents opposed to the clerical regime in Tehran.
Iraq's government is officially neutral on the Syrian civil war and it has called for a negotiated political solution. Iraq's Shiite leadership has bolstered ties with Shiite heavyweight Iran in the years since the 2003 U.S.-led invasion, and it is concerned about the threat posed by Sunni extremists, including Iraq's al-Qaida branch, fighting among the rebels
Other Iraqi Shiite militias with ties to Tehran are talking tough, including the Hezbollah Brigades, which has claimed responsibility for previous attacks on U.S. troops in Iraq. It said recently that American and allied interests "must be removed from the region."
Asaib Ahl al-Haq, an Iranian-backed hard-line faction that also carried out deadly attacks against U.S. troops before their withdrawal, said in a statement this week that action against Syria "will set the region on fire. The interests of the Western countries will not be saved from this fire."
A senior Asaib Ahl al-Haq official said multiple armed groups within Iraq are "fully prepared to respond to any strike on Syria by attacking the interests of the countries that participate in this strike, including the United States," although he declined to specify any potential targets.
The Asaib Ahl al-Haq official, who refused to be identified, fearing retribution, said the militias are awaiting instructions from Iran's supreme leader, Ayatollah Ali Khamenei, on the timing and method of any attacks.
U.S. Embassy spokesman Rodney Ford did not address the threats specifically, saying he can't comment on intelligence matters.
"We have long-standing concerns about Iran's destabilizing influence in the broader region and will continue to work with our partners to address these activities," he said, without elaborating.
Iranian officials in Tehran did not return calls seeking a response on Friday.
The Wall Street Journal reported in its Friday edition that the U.S. has intercepted an order from Gen. Ghasem Soleimani, the head of the Iranian Revolutionary Guard's elite Quds Force, telling Iraqi militias to prepare to strike American interests inside Iraq. The Journal report quoted unnamed American officials, who said the U.S. Embassy was one potential target.
The Quds Force oversees external operations of the Guard throughout the world.
One senior Iraqi intelligence official said authorities have indications that militants are planning responses against American interests and other targets, but he declined to provide details. Another top intelligence official said that Iranian-backed militants have the ability to target sites such as the U.S. Embassy with rockets. Both officials insisted on anonymity because they weren't authorized to discuss intelligence matters.
Ali al-Moussawi, the spokesman for Prime Minister Nouri al-Maliki, said Iraq remains concerned about a possible military strike on Syria and reactions to it might bring in Iraq and the wider region. He was unable to provide details about any threats against the U.S. Embassy but said the government takes seriously its responsibility to protect diplomatic missions and other American interests.
"Our reaction will be strong and firm. The Iraqi government will not tolerate any groups that might be involved in such attacks, which are considered an aggression on Iraq's sovereignty," he said.
John Drake, an Iraq specialist for the British-based AKE security consulting firm, said Iranian-backed militants could respond to a Syria strike by attacking consular facilities with roadside bombs or indirect fire such as rockets and mortar shells.
"Indirect fire is often used as a tactic against facilities which are otherwise well defended," he said. It can also be very inaccurate, hitting unintended targets, he noted.
Western oil and gas facilities in Iraq's southern Shiite heartland might also be potential targets, although an attack on the lucrative energy sector "would harm the Iraqi government, which is something Tehran would want to avoid," he said.
The latest threats emerged as the U.S. State Department released an updated travel alert warning that Americans remain at high risk for kidnapping and terrorist attacks inside Iraq.
The alert did not specifically address the risks from Iranian-backed militants, although it noted that numerous insurgent groups are active and said "terrorist activity and sectarian violence persist in many areas of the country at levels unseen since 2008."
Violence in Iraq has been accelerating since April, with more than 4,000 killed in terrorist attacks over the past five months.
Sectarian tensions that are fueling the violence are being exacerbated by the civil war in Syria. Mainly Sunni rebels there are fighting to topple President Bashar Assad's Iranian-backed regime, which is dominated by Alawites, an offshoot of Shiite Islam.