BAGHDAD/WASHINGTON (Reuters) - U.S. President Donald Trump on Saturday threatened to hit 52 Iranian sites “very hard” if Iran attacks Americans or U.S. assets after a drone strike that killed Iranian military commander Qassem Soleimani and an Iraqi militia leader, as tens of thousands of people marched in Iraq to mourn their deaths.

Showing no signs of seeking to ease tensions raised by the strike he ordered that killed Soleimani and Iranian-backed Iraqi militia leader Abu Mahdi al-Muhandis at Baghdad airport on Friday, Trump issued a threat to Iran on Twitter. The strike has raised the specter of wider conflict in the Middle East.

Iran, Trump wrote, “is talking very boldly about targeting certain USA assets” in revenge for Soleimani’s death. Trump said the United States has “targeted 52 Iranian sites” and that some were “at a very high level & important to Iran & the Iranian culture, and those targets, and Iran itself, WILL BE HIT VERY FAST AND VERY HARD.”

“The USA wants no more threats!” Trump said, adding that the 52 targets represented the 52 Americans who were held hostage in Iran for 444 days after being seized at the U.S. Embassy in Tehran in November 1979 - an enduring sore spot in U.S.-Iranian relations.

Trump did not identify the sites. The Pentagon referred questions about the matter to the White House, which did not immediately respond to a request for comment.

Among the mourners in Iraq included many militiamen in uniform for whom Muhandis and Soleimani were heroes. They carried portraits of both men and plastered them on walls and armored personnel carriers in the procession. Chants of “Death to America” and “No No Israel” rang out.

On Saturday evening, a rocket fell inside Baghdad’s heavily fortified Green Zone near the U.S. Embassy, another hit the nearby Jadriya neighborhood and two more were fired at the Balad air base north of the city, but no one was killed, Iraq’s military said. There was no immediate claim of responsibility.

Trump referenced an unusually specific number of potential Iranian targets after a senior Iranian Revolutionary Guards commander had also mentioned a specific number of American targets - 35 of them - for possible retaliatory attacks in response to Soleimani’s killing.

General Gholamali Abuhamzeh was quoted by Tasnim news agency as saying late on Friday that Iran will punish Americans wherever they are within reach of the Islamic Republic, and raised the prospect of attacks on ships in the Gulf.

“The Strait of Hormuz is a vital point for the West and a large number of American destroyers and warships cross there. ... Vital American targets in the region have been identified by Iran since long time ago. ... Some 35 U.S. targets in the region as well as Tel Aviv are within our reach,” he was quoted as saying.

Iraq’s Kataib Hezbollah militia warned Iraqi security forces to stay away from U.S. bases in Iraq, “by a distance not less than a thousand meters (six-tenths of a mile) starting Sunday evening,” reported Lebanese al-Mayadeen TV, which is close to Lebanon’s Hezbollah.

Trump said on Friday Soleimani had been plotting “imminent and sinister” attacks on American diplomats and military personnel. Democratic critics said the Republican president’s action was reckless and risked more bloodshed in a dangerous region.

‘MALIGN INFLUENCE’

Trump’s provocative Twitter posts came only hours after U.S. Secretary of State Mike Pompeo wrote on Twitter that he had told Iraq’s president that “the U.S. remains committed to de-escalation.” Pompeo also wrote on Twitter that he had spoken with Israeli Prime Minister Benjamin Netanyahu about Iran and “underscored the importance of countering Iran’s malign influence and threats to the region.”

The White House on Saturday sent to the U.S. Congress formal notification of the drone strike - as required by law - amid complaints from Democrats that Trump did not notify lawmakers or seek advance approval for the attack. White House national security adviser Robert O’Brien defended the operation’s legality and said Justice Department lawyers had signed off on the plan.

Democrats sounded unswayed. House of Representatives Speaker Nancy Pelosi said the notification document raised “serious and urgent questions about the timing, manner and justification” of the strike.

Democratic Representative Alexandria Ocasio-Cortez, a strident Trump critic, wrote on Twitter that his threat to hit Iranian sites “is a war crime.”

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“Threatening to target and kill innocent families, women and children - which is what you’re doing by targeting cultural sites - does not make you a ‘tough guy.’ It does not make you ‘strategic.’ It makes you a monster,” Ocasio-Cortez wrote.

With security worries rising after Friday’s strike, the NATO alliance and a separate U.S.-led mission suspended their programs to train Iraqi security and armed forces, officials said.

Soleimani, 62, was Iran’s pre-eminent military leader - head of the Revolutionary Guards’ overseas Quds Force and the architect of Iran’s spreading influence in the Middle East. Muhandis was de facto leader of Iraq’s Popular Mobilisation Forces (PMF) umbrella body of paramilitary groups.

The attack took Washington and its allies, mainly Saudi Arabia and Israel, into uncharted territory in their confrontation with Iran and its proxy militias across the region.

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The United States has been an ally of the Iraqi government since the 2003 U.S. invasion to oust dictator Saddam Hussein, but Iraq has become more closely allied with Iran.

The Iraqi parliament is convening an extraordinary session during which a vote to expel U.S. troops could be taken as soon as Sunday. Many Iraqis, including opponents of Soleimani, have expressed anger at Washington for killing the two men on Iraqi soil and possibly dragging their country into another conflict.

BODIES TAKEN TO HOLY CITIES

A PMF-organized procession carried the bodies of Soleimani and Muhandis, and those of others killed in the U.S. strike, through Baghdad’s Green Zone.

The top candidate to succeed Muhandis, Hadi al-Amiri, spoke over the dead militia commander’s coffin: “The price for your noble blood is American forces leaving Iraq forever and achieving total national sovereignty.”

Prime Minister Adel Abdul Mahdi also attended. Mahdi’s office later said he received a phone call from Saudi Crown Prince Mohammed bin Salman and they “discussed the difficult conditions facing Iraq and the region.”

Mourners brought the bodies of the two slain men by car to the Shi’ite holy city of Kerbala, south of Baghdad, then to Najaf, another sacred Shi’ite city, where they were met by the son of Iraq’s top Shi’ite cleric, Grand Ayatollah Ali al-Sistani, and where Muhandis and the other Iraqis killed will be laid to rest.

Soleimani’s body will be transferred to the southwestern Iranian province of Khuzestan that borders Iraq. On Sunday it will be taken to the Shi’ite holy city of Mashhad in Iran’s northeast and from there to Tehran and his hometown Kerman in the southeast for burial on Tuesday, state media said.

The U.S. strike followed a sharp increase in U.S.-Iranian hostilities in Iraq since last week when pro-Iranian militias attacked the U.S. embassy in Baghdad after a deadly U.S. air raid on Kataib Hezbollah, founded by Muhandis. Washington accused the group of an attack on an Iraqi military base that killed an American contractor.