"Don't think that everything is over with my father's martyrdom," Zeinab Soleimani said. (AFP)

Hundreds of thousands of Iranians thronged Tehran's streets on Monday for the funeral of military commander Qassem Soleimani, killed by a U.S. drone strike last week, and his daughter said his death would bring a "dark day" for the United States.

"Crazy Trump, don't think that everything is over with my father's martyrdom," Zeinab Soleimani said in an address broadcast on state television.

U.S. President Donald Trump had ordered Friday's attack that killed the general, the architect of Iran's drive to extend its influence across the region. Iran has promised to avenge his death.

The size of the crowds in Tehran, shown on television and which state media said numbered in the millions, mirrored the masses that gathered in 1989 for the funeral of the Islamic Republic's founder, Ayatollah Ruhollah Khomeini.

Soleimani was a national hero to many Iranians, even those who did not consider themselves devoted supporters of Iran's clerical rulers.

In response to Iran's warnings of retaliation, Trump has threatened to hit 52 Iranian sites, including cultural targets, if Tehran attacks Americans or U.S. assets, deepening a crisis that has heightened fears of a new Middle East conflagration.

Iran's supreme leader Ayatollah Ali Khamenei presided over prayers for the killed general. (AFP)

The coffins of Soleimani and Iraqi militia leader Abu Mahdi al-Muhandis, who was also killed in the strike, were passed across the heads of mourners chanting "Death to America".

Aerial footage showed crowds packed thoroughfares and sidestreets in central Tehran, a welcome show of national unity for the government after deadly protests in November.

Influence

One of Iran's main regional goals - driving U.S. forces out of neighbouring Iraq - came a step closer on Sunday when the Iraqi parliament backed a recommendation by the prime minister for all foreign troops to be ordered out.

"Despite the internal and external difficulties that we might face, it remains best for Iraq on principle and practically," Iraqi caretaker Prime Minister Adel Abdul Mahdi said.

Iraq's rival Shi'ite leaders, including ones opposed to Iranian influence, have united since Friday's attack in calling for the expulsion of U.S. troops. About 5,000 U.S. military personnel are in Iraq, mostly acting as advisers.

Esmail Qaani, the new head of the Quds Force, the Revolutionary Guards' unit in charge of foreign operations, said Iran would continue Soleimani's path.

Soleimani built up Iran's network of proxy regional forces, creating a crescent of influence stretching from Lebanon through Syria and Iraq to Iran. Allies also include Palestinian and Yemeni groups.

Prayers at Soleimani's funeral in Tehran, which will later move to his southern home city of Kerman, were led by Iranian Supreme Leader Ayatollah Ali Khamenei, who wept as he spoke. Soleimani was widely seen as the second most powerful figure in Iran behind Khamenei.

Ismail Haniyeh, leader of Palestinian terror group Hamas, made his first trip to Iran since taking up his role in 2017 in order to attend.

"Resistance against the Zionist project on the land of Palestine will not stop, and resistance against the American dominance will not be broken and will not be weakened," Haniyeh said, referring to Israel.

Nuclear Tensions

Adding to tensions, Iran said it was taking another step back from commitments under a 2015 nuclear deal with six powers, which the United States withdrew from in 2018.

Germany said Iran's move to abandon limitations on enriching uranium could end the pact, which European governments have been trying to stop from collapsing.

Since quitting it, the United States has imposed new sanctions on Iran, describing its policy as "maximum pressure" and saying it wanted to drive down Iranian oil exports - the main source of government revenues - to zero. Iran's economy has been in freefall as the currency has plunged in value.

Talking to reporters on Sunday, Trump stood by his remarks to include cultural sites on his list of potential targets, despite drawing criticism from U.S. politicians.

"They're allowed to kill our people. 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 sites? It doesn't work that way," Trump said.

Democratic critics of the Republican president have said Trump was reckless in authorising the strike. Some said his comments about targeting cultural sites amounted to threats to commit war crimes. Many asked why Soleimani, long seen as a threat by U.S. authorities, had to be killed now.

Republicans in the U.S. Congress have generally backed Trump's move.

Trump also threatened sanctions against Iraq and said that if U.S. troops were required to leave the country, Baghdad would have to pay Washington for the cost of a "very extraordinarily expensive" air base there.

It was not clear if Washington had advised any of its allies of its plans prior to the attack. Britain, which also has troops in Iraq, said it understood why the United States had killed Soleimani but urged a de-escalation of tensions to avoid war in the Middle East.

Oil prices jump 2% on Monday, rising above $70 a barrel, on concerns about an escalation.