Members of the Iranian-backed militia Kataib Hezbollah were responsible for Sunday’s rocket attack that landed near U.S. military and diplomatic outposts in Baghdad’s Green Zone, Iraqi counterterrorism officials say.

Top officials with the country’s Counter Terrorism Services told the Daily Beast on Monday that the paramilitary group launched the Katyusha rocket landed near the parade grounds inside the heavily-fortified Green Zone, which is home to the U.S. embassy as well as the main headquarters for the American-led coalition battling the Islamic State.

Iraqi officials say the attack was designed as a singular strike, designed as a way to test U.S. defenses in and around key installations in Iraq, but stopped short of the kind of strike that would trigger an American military response, according to reports.

The Shi’ite militia, which has long had strong ties to the Iranian regime, denied the accusations on social media Monday, saying Sunday’s rocket attack was “unjustified, its timing inappropriate, and it does not serve the public interest.”

Other Shia militias affiliated with Iran also vehemently denied any involvement on the Green Zone strike. Qais al-Khazali, leader of Iranian-backed Asaib Ahl al-Haq said in a Twitter post warned against any U.S. response that could further engulf Iraq in a proxy war between Tehran and the West.

“We warn against the mixing of cards that are intended to create pretexts for war and are intended to damage Iraq’s political, economic and security situation,” Mr. al-Khazali said shortly after the attack Sunday.

The paramilitary group’s spokesman, Naeem al-Aboudi, suggested the attack could have been the work of Islamic State sleeper cells operating in Baghdad, in an attempt to stoke conflict between Washington and Tehran, the online news outlet Middle East Eye reported.

On Monday, South Carolina Republican Sen. Lindsey Graham said the White House has presented evidence that Iran “over the last several weeks … has attacked pipelines and ships of other nations and created threat streams against American interests in Iraq.”

“If the Iranian threats against American personnel and interests are activated we must deliver an overwhelming military response,” Mr. Graham said shortly after being briefed by White House National Security Adviser John Bolton.

Mr. Trump took to Twitter hours after the Sunday attack, threatening Tehran from taking any action against U.S. interests in Iraq or elsewhere in the region. “if Iran wants to fight, that will the official end of Iran. Never threaten the United States again,” he said.

State Department officials acknowledged in a separate statement that no entity had yet taken responsibility for the attacks, but that Washington would hold Tehran accountable should its Iraqi proxies be deemed responsible for the strike.

No casualties were reported as a result of the Green Zone attack and no group has yet to officially claimed responsibility for the strikes.

The Green Zone strikes come days after the Trump administration ordered the withdrawal of all non-essential personnel from U.S. outposts in Baghdad, due to communications intercepted by U.S. intelligence related to the movement of rockets in Iraq by Iran-backed militias in the city.

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