* Iraqi mourners shout 'Death to America' and 'No No Israel'
* U.S. urges citizens to leave Iraq on security grounds
* Any Americans 'within reach' to be punished -Iran officer
* Cites 35 possible targets including Gulf oil region
* (Adds reaction in Iran)
By Ahmed Aboulenein and Maha El Dahan
BAGHDAD, Jan 4 (Reuters) - Tens of thousands of people marched in Baghdad on Saturday to mourn Iran's military chief Qassem Soleimani and Iraqi militia leader Abu Mahdi al-Muhandis, killed in a U.S. air strike that has raised the spectre of wider conflict in the Middle East.
By ordering Friday's strike on the commander of the Iranian Revolutionary Guard's foreign legions, President Donald Trump has taken Washington and its allies, mainly Saudi Arabia and Israel, into uncharted territory in its confrontation with Iran and its proxy militias across the region.
Gholamali Abuhamzeh, a senior commander of Iran's elite Revolutionary Guards, said Tehran would punish Americans "wherever they are in reach", and raised the prospect of possible attacks on ships in the Gulf.
The U.S. Embassy in Baghdad urged American citizens to leave Iraq following the strike at Baghdad airport that killed Soleimani. Dozens of American employees of foreign oil companies left the southern Iraqi city of Basra on Friday.
Close U.S. ally Britain warned its nationals on Saturday to avoid all travel to Iraq, outside the autonomous Kurdistan region, and to avoid all but essential travel to Iran.
The United States and its allies have suspended training of Iraqi forces due to the increased threat, the German military said in a letter seen by Reuters late on Friday.
Soleimani, a 62-year-old general, was Tehran's pre-eminent military commander and - as head of the Revolutionary Guards' overseas Quds Force - the architect of Iran's spreading influence in the Middle East.
Muhandis was the deputy commander of Iraq's Popular Mobilisation Forces (PMF) umbrella body of paramilitary groups.
A PMF-organised procession carrying the bodies of Soleimani, Muhandis and other Iraqis killed in the U.S. strike took place in Baghdad's heavily fortified 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 armoured personnel carriers in the procession, and chanted, "Death to America" and "No No Israel".
Prime Minister Adel Abdul Mahdi and Iraqi militia commander Hadi al-Amiri, a close Iran ally and the top candidate to succeed Muhandis, attended.
Mourners later brought the bodies of those killed in the strike by car to the Shi'ite holy city of Kerbala south of Baghdad. The procession was to end in Najaf, another sacred Shi'ite city where Muhandis and the other Iraqis killed will be laid to rest.
Soleimani's body will be transferred on Saturday 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.
Trump said on Friday Soleimani had been plotting imminent attacks on American diplomats and military personnel. Democratic critics of the Republican president said Trump's action was reckless and that he had aggravated the risk of more bloodshed in a dangerous region.
The U.S. strike followed a sharp increase in U.S.-Iranian hostilities in Iraq since last week when pro-Iranian militia attacked the U.S. Embassy in Baghdad after a deadly U.S. air raid on the Kataib Hezbollah militia, founded by Muhandis.
'VITAL AMERICAN TARGETS'
On Friday, Iranian Supreme Leader Ayatollah Ali Khamenei vowed to retaliate and said Soleimani's death would intensify the Islamic Republic's resistance to the United States and Israel.
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.
"Vital American targets in the region have long since been identified by Iran...Some 35 U.S. targets in the region as well as Tel Aviv are within our reach," he said, referring to Israel's largest city.
In Iran, some people worried that Soleimani's death might push the country into ruinous war with a superpower.
"I feel so sad for Soleimani's death but what if America and Iran start a war? I have children. What if they send my (university student) son to war?" said Monireh, a retired teacher.
Mohamed Raad, a political leader in Lebanon's heavily armed Hezbollah movement, said retaliation by the Iran-backed "axis of resistance" - militia groups in countries from Lebanon to Yemen - would be decisive, al-Mayadeen TV reported on Saturday.
'REVENGE ON THE MURDERERS'
Many Iraqis condemned the U.S. attack, regarding Soleimani as a hero for his role in defeating Islamic State militants who seized large swathes of north and central Iraq in 2014.
"It is necessary to take revenge on the murderers. The martyrs got the prize they wanted - the prize of martyrdom," said one of the marchers, Ali al-Khatib.
Many Iraqis also voiced fear of being engulfed in a major U.S.-Iranian conflict, and of militia reprisals against those involved in months of street protests against the Iranian-backed Baghdad government over alleged misrule and corruption.
They said Soleimani and Muhandis had backed the use of force against unarmed anti-government protesters last year and established militias that demonstrators blame for many of Iraq's social and economic woes.
(Reporting by Ahmed Aboulenein and Maha El Dahan Additional reporting by Kate Holton in London, Parisa Hafezi in Dubai and Nadine Awadallah in Beirut Writing by Mark Heinrich Editing by Frances Kerry)
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