By Ahmed Aboulenein and Maha El Dahan
BAGHDAD (Reuters) - With shouts of "Death to America", tens of thousands of people marched in Iraq on Saturday to mourn Iranian military commander Qassem Soleimani and an Iraqi militia leader who were killed in a U.S. air strike that has raised the specter of wider conflict in the Middle East.
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 rockets were fired at the Balad air base north of the city, but no one was killed, the Iraqi military said in a statement. There was no immediate claim of responsibility.
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.
"The safety of our personnel in Iraq is paramount. We continue to take all precautions necessary," acting NATO spokesman Dylan White said in a statement.
Soleimani, commander of the Revolutionary Guards' foreign legions, was killed in the U.S. strike on his convoy at Baghdad airport. Iranian-backed Iraqi militia leader Abu Mahdi al-Muhandis was also killed. 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.
France stepped up diplomatic initiatives on Saturday to ease tensions. French President Emmanuel Macron talked with Iraq President Barham Salih, Macron's office said.
"The two presidents agreed to remain in close contact to avoid any further escalation in tensions and in order to act to ensure stability in Iraq and the broader region," a statement from Macron's office said.
Macron also spoke with the de facto ruler of the United Arab Emirates, Abu Dhabi Crown Prince Sheikh Mohammed bin Zayed al-Nahyan.
Gholamali Abuhamzeh, a senior commander of the Revolutionary Guards, said Tehran would punish Americans "wherever they are in reach", and raised the prospect of possible attacks on ships in the Gulf.
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 starting Sunday evening," reported Lebanese al-Mayadeen TV, which is close to Lebanon's Hezbollah.
VOTE ON U.S. TROOP PRESENCE
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 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."
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.
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.
A PMF-organised procession carried the bodies of Soleimani and Muhandis, and those of others killed in the U.S. strike, through Baghdad's Green Zone.
Mourners 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.
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."
BODIES TAKEN TO HOLY CITIES
Mourners later brought the bodies 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.
U.S. President Donald Trump said on Friday that 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.
Some U.S. national security and congressional officials questioned the use of the word imminent to justify the killing, while some legal experts and a senior U.N. rights investigator said the strike could have violated international law.
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.
Abuhamzeh, the Revolutionary Guards commander in Kerman province, mentioned a series of possible targets for reprisals including the Gulf waterway through which about a third of the world's shipborne oil is exported to global markets.
"The Strait of Hormuz is a vital point for the West and a large number of American destroyers and warships cross there," Abuhamzeh was quoted as saying on Friday evening by the semi-official news agency Tasnim.
British defense minister Ben Wallace said on Saturday he had ordered Britain's navy to accompany all UK-flagged ships through the Strait of Hormuz to provide protection.