An $80 million bounty has reportedly been placed on Donald Trump's head following the assassination of General Qasem Soleimani.

The chilling announcement was broadcast live as millions of Iranians took to the streets for Soleimani's televised funeral.

"Iran has 80 million inhabitants. Based on the Iranian population, we want to raise $80 million, which is a reward for those who get close to the head of President Trump," the eulogist at the funeral procession said, according to Saudi free-to-air network Al Arabiya.

The funeral procession was being broadcast live on Iran's Channel One as the eulogist made this statement.

Iran has vowed to inflict "harsh revenge" on the USA after its politicians dramatically opened parliament chanting "death to America" in response to "a declaration of war".

Iran reportedly threatened to attack the White House while branding Trump a "terrorist in a suit" after he vowed to hit dozens of targets in the Islamic Republic.

Flag draped coffins of General Qassem Soleimani and his comrades who were killed in Iraq in a US drone strike, carried on a truck surrounded by mourners. Photo / AP

Iranian Labour News Agency claimed Iranian MP Abolfazl Abutorabi issued the threats during an open session of parliament on Sunday.

"We can attack the White House itself, we can respond to them on the American soil," he said, according to reports.

"We have the power, and God willing we will respond in an appropriate time.

The comments came after Trump issued a stark warning to Iran threatening order "very fast and very hard" strikes in the Islamic Republic if it retaliates for the targeted killing of General Qassem Soleimani. The leader of Iran's expeditionary Quds Force that organises Tehran's proxy forces in the wider Mideast was killed by the US in Baghdad on Friday.

Late Saturday, a series of rockets launched in Baghdad fell inside or near the Green Zone, which houses government offices and foreign embassies, including the US Embassy.

Trump tweeted afterwards that his administration had already "targeted 52 Iranian sites (representing the 52 American hostages taken by Iran many years ago), some at a very high level & important to Iran & the Iranian culture".

Trump did not identify the targets but added that they would be "HIT VERY FAST AND VERY HARD".

Soleimani's killing escalated the crisis between Tehran and Washington after months of trading attacks and threats that have put the Middle East on edge. Tensions have been simmering since Trump pulled out of Iran's atomic accord and imposed sanctions that have crippled the country's economy.

Iran has promised "harsh revenge" for the latest US attack, which shocked Iranians across all political lines. Many saw Soleimani as a pillar of the Islamic Republic at a moment when it is beset by US sanctions and recent anti- government protests.

Telecommunications minister Mohammad Javad Azari Jahromi compared Trump's threats to the Islamic State group, Adolf Hitler and Genghis Khan. "They all hate cultures. Trump is a 'terrorist in a suit'," Jahromi wrote on Twitter.

"He will learn history very soon that NOBODY can defeat the Great Iranian Nation & Culture."

Trump later hit back: "The United States just spent Two Trillion Dollars on Military Equipment. We are the biggest and by far the BEST in the World!

"If Iran attacks an American Base, or any American, we will be sending some of that brand new beautiful equipment their way … and without hesitation!"

Iran's Foreign Minister Mohammed Javad Zarif wrote on Twitter Sunday that after committing "grave breaches" in the killing of Soleimani, Trump is threatening new breaches of international law.

Zarif wrote: "Targeting cultural sites is a WAR CRIME."

Parliament speaker Ali Larijani on Sunday compared Soleimani's killing to the 1953 CIA-backed coup that cemented the shah's power and to the US Navy's shootdown of an Iranian passenger plane in 1988 that killed 290 people. He also described American officials as following "the law of the jungle."

Soleimani was the architect of Iran's regional policy of mobilising militias across Iraq, Syria and Lebanon, including in the war against the Islamic State group. He was also blamed for attacks on US troops and American allies going back decades.

The leader of Lebanon's Hezbollah said Soleimani's killing made US military bases, warships and service members spread across the region fair targets for attacks. The US Embassy in Saudi Arabia separately warned Americans "of the heightened risk of missile and drone attacks". Meanwhile, Iraq's parliament voted in favour of a resolution calling for an end of the foreign military presence in their nation, an effort aimed at expelling the 5,000 US troops stationed there over the war against the Islamic State group.

Iran's state television later reported that the country will no longer abide by any of the limits of its 2015 nuclear deal.

Mourners step over US flags under a picture of Iranian general Qasem Soleimani who was killed in an American air strike in Iraq. Photo / AP

The announcement came Sunday night after another Iranian official said it would consider taking even-harsher steps over the US killing of Soleimani. State TV cited a statement by Iranian President Hassan Rouhani's administration saying the country will not observe limitations on its enrichment, the amount of stockpiled enriched uranium as well as research and development in its nuclear activities.

It did not elaborate on what levels it would immediately reach in its program. The International Atomic Energy Agency, the United Nations watchdog observing Iran's program, could not be immediately reach for comment.

US Secretary of State Mike Pompeo insisted Soleiman's assassination has made the world safer, and that taking no action would have created more risk.

Pompeo's comments - in an interview on ABC's This Week - follow reports some senior White House officials were sceptical about the rationale for the drone strike.

"The intelligence assessment made clear that no action - allowing Soleimani to continue his plotting and his planning, his terror campaign - created more risk than taking the action that we took last week," Pompeo said.

"This was a bad guy, we took him off the playing field.

"And that's important because this was a fella who was the glue, who was conducting active plotting against the United States of America, putting American lives at risk."

Although it's unclear how or when Iran may respond in full, any retaliation was likely to come after three days of mourning declared in both Iran and Iraq for Soleimani.