Trump ordered a US drone to fire a missile at Soleimani, one of the most influential people in Iran’s government, when he was near the Iraqi capital’s international airport.

Angry, black-clad mourners thronged the streets of Iran’s second city Mashhad on Sunday to pay last respects to the remains of Soleimani and chant “death to America”.

Trump bluntly warned Iran against taking vengeance, repeating his insistence that US bombing targets could include Iran’s cultural heritage sites. Critics say that would qualify as a war crime under international law.

“If they do anything there will be major retaliation,” Trump told reporters on Air Force One, as he flew back to Washington - and a looming Senate impeachment trial - from holiday in Florida.

In his latest comments, he was adamant that targets could include places of cultural significance in a country boasting an ancient heritage and two dozen Unesco-listed sites.

“They’re allowed to kill our people,” a defiant Trump said. “They’re allowed to torture and maim our people. They’re allowed to use roadside bombs and blow up our people. And we’re not allowed to touch their cultural site? It doesn’t work that way.”

The situation in neighbouring Iraq, a US ally, also deteriorated, with the future of some 5,200 American soldiers there in doubt.

Many Iraqis have expressed outrage over the killing of Soleimani, who masterminded deep Iranian influence in the country. A top Iraqi military figure Abu Mahdi al-Muhandis was killed in the same US strike.

Thousands in Iran mourn slain general Qassem Soleimani, chanting ‘Death to America’

In Baghdad, unidentified attackers launched a pair of rockets Sunday, hitting near the US embassy in the high-security Green Zone for the second night in a row. That was just hours after Iraq’s foreign ministry summoned the American ambassador over the drone strike.

And Iraq’s parliament voted to request the government end an agreement with a US-led international coalition to fight the hardline Islamic State (Isis) in the region.

If the government agreed, that would effectively require the departure of US soldiers supporting the local troops in the anti-Isis fight.

Caretaker prime minister Adel Abdel Mahdi, who called the US drone strike a “political assassination”, indicated he would back the troops’ ouster. He said the choices were immediate expulsion or withdrawal under a timeframe.

Trump told reporters that a forced departure of US troops would prompt sanctions even worse than those already imposed, to devastating effect, on Iran’s economy.

“If they do ask us to leave - if we don’t do it in a very friendly basis - we will charge them sanctions like they’ve never seen before,” Trump said.

Chinese embassy in US issues safety warning as tensions rise over killing of Iran’s military chief Qassem Soleimani

“It’ll make Iranian sanctions look somewhat tame.”

Trump said the main US base in Iraq was “very extraordinarily expensive.”

“We’re not leaving unless they pay us back for it,” he said.

Earlier, US Secretary of State Mike Pompeo sounded a softer note, saying “the Iraqi people want the United States to continue to be there to fight the counterterror campaign.”

Soleimani was one of Iran’s most popular public figures, seen as a hero of the 1980-88 Iran-Iraq war.

He was also the key figure behind Iran’s effective network of proxy militias and alliances across a region where Iran is in often deadly rivalry with US allies Israel and Saudi Arabia.

Iran’s supreme leader Ayatollah Ali Khamenei has vowed “severe revenge”.

What that will look like is the subject of heated speculation in the Pentagon and the White House. Analysts say Iran may be limited in its room for maneuver if it wants to avoid full war with the far more powerful United States.

Qassem Soleimani was Iran’s ‘living martyr’ who saw long war against US and Israel as ‘lost paradise’

But a former head of Iran’s Revolutionary Guards threatened on Sunday to turn the Israeli cities of Haifa and Tel Aviv “to dust” if the US attacks targets in Iran.

And Khamenei’s military adviser, Brigadier General Hossein Dehghan, told CNN that Iran’s response to the assassination “for sure will be military and against military sites”.

The crisis comes as Trump is embroiled in his own domestic political turmoil. He was impeached by the House of Representatives for abuse of office and obstruction of Congress.

The Senate, where his Republican party has a commanding majority, is wrangling over when and how a trial will take place, as the clock ticks down on the November presidential elections.

Additional reporting by Bloomberg