WASHINGTON (AFP) -- President Donald Trump sought Tuesday to end confusion over the future of American troops in Iraq, saying they should stay, despite fury there over the US killing of a top Iranian general in Baghdad.

"At some point we want to get out, but this isn't the right point," Trump told reporters at the White House.

Regardless of US efforts to clarify the troops' future following an Iraqi parliament call for their exit, regional tension and uncertainty increased.

In the Iranian city of Kerman, more than 50 people died in a stampede by a crowd attending the funeral of slain Revolutionary Guards commander Qasem Soleimani, Iranian media reported.

The hugely influential figure was killed in a US drone strike on Friday near Baghdad's international airport and had been due to be buried in his home town when the crowd got out of control.

The tragedy added to the sense of volatility triggered by Soleimani's killing, with crowds in Iran chanting "death to America" and Tehran and Washington exchanging warnings of war.

Trump, however, did walk back earlier threats to bomb Iranian cultural sites in the event of conflict -- something that could be a war crime.

"If that's what the law is, I like to obey the law," Trump said.

Foreign troops waver

At the Soleimani funeral, top Revolutionary Guards commander Major General Hossein Salami said Iran would "take revenge."

If further US attacks occur, "we will set fire to what they love," he said.

In Washington, Defense Secretary Mark Esper said "we should expect" Iran to go through with threats.

Trump said "we are totally prepared."

"If Iran does anything that they shouldn't be doing, they're going to be suffering the consequences and very strongly," Trump said, calling Soleimani "a monster."

Fallout from Soleimani's killing also piled up in Iraq, where Iran has growing influence.

Despite Washington's assurances that the approximately 5,200 US troops will remain in Iraq, several allies started to leave, raising questions over the future of a US-led mission to help the Iraqis fight the jihadist Islamic State group.

Canada announced that some of its estimated 500 troops will withdraw to Kuwait. And NATO, which suspended its training mission in Iraq after the killing, said it also was temporarily "repositioning" some personnel to locations inside and outside Iraq.

Several other countries, including Germany and Romania, announced plans to move forces. France said it had no intention of withdrawing its troops from Iraq.

Italy also said that after a "frank and articulate" phone call between Defense Minister Lorenzo Guerini and US Defense Secretary Mark Esper that its approximately 1,000 soldiers in the country would stay.

US attempts to clarify

On Sunday the Iraqi parliament voted in favor of expelling US troops in response to Soleimani's killing.

Then on Monday, a letter emerged from the head of Task Force-Iraq, US Brigadier General William Seely, that appeared to announce just such an exit.

Back in Washington, US officials scrambled to deny the idea, calling the letter a mistakenly released draft or, as Trump suggested, a fake.

"I don't know anything about that letter," Trump told reporters. "I understand it was an unsigned letter. I don't know if that letter was a hoax, or was it unsigned or what."

Iraq's prime minister, however, insisted Tuesday that the letter had been taken seriously.

"It was an official letter written in such a manner," Abdel Mahdi told a televised cabinet meeting.

"It's not a piece of paper that fell off the printer or reached us by coincidence," he said.

Attempting to draw a line under the issue, Esper said that "policy has not changed. We are not leaving Iraq."

He also insisted that there was "no signed letter, to the best of my knowledge."

Trump said he favored eventual withdrawal from Iraq but that under the wrong conditions it would mean a strategic gift to Iran.

"If we leave, that would mean that Iran would have a much bigger foothold, and the people of Iraq do not want to see Iran run the country. That I can tell you," Trump told reporters.

"It's the worst thing that could happen to Iraq."

Crushed under crowd

An additional 212 people were injured in the Kerman stampede, Iran's semi-official news agency ISNA said, citing officials in the southeastern city.

Anxious Iranians gathered outside a city hospital to check the lists of victims or show doctors pictures of their missing relatives.

Inside, patient Ali Salaji, 28, recounted the crush as his mother tended to him.

"I could hardly breathe. I had a seizure, and my foot was crushed pretty bad under the weight of all that crowd," he told AFP.

The streets of Kerman overflowed with mourners, while others took refuge on hillsides around the city, where the general was to be buried at the martyrs' cemetery.

After the stampede, Iranian media stopped broadcasting live from the cemetery, with some outlets suggesting the burial might not take place before morning. (AFP)