US President Donald Trump thumbed his nose on Sunday at critics angered at being kept in the dark over the US killing of a top Iranian general, saying he didn't need congressional approval — even for a "disproportionate" strike.

House Speaker Nancy Pelosi has been leading the backlash against Trump's decision to authorise a drone strike against Qasem Soleimani in Baghdad, an operation that Trump only officially informed Congress about on Saturday — nearly 48 hours after the event.

Pelosi said the House will introduce and vote on a war powers resolution this week to limit Trump's military actions regarding Iran.

"This resolution is similar to the resolution introduced by Senator Tim Kaine in the Senate," Pelosi said in a statement late on Sunday.

"It reasserts Congress's long-established oversight responsibilities by mandating that if no further congressional action is taken, the administration's military hostilities with regard to Iran cease within 30 days."

The resolution is likely to win approval in the Democratic-led House, but prospects for passage are less certain in the Senate, which is controlled by Trump's fellow Republicans, many of whom have said they support the president's action on Iran.

Iraq's parliament called for the US and other foreign troops to leave as the backlash against the US killing on Friday of Soleimani grew, and Trump doubled down on threats to target Iranian cultural sites if Iran retaliates.

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

Two Democratic lawmakers also announced on Sunday that they would introduce a new resolution before the House of Representatives that they said would prevent Trump from unilaterally leading the United States into a war against Iran.

But a defiant Trump made light of the calls for him to get congressional approval in any future military action, saying such notice was "not required" — and then saying his tweet would serve as prior notification if he did decide to strike against Iran again.

"These Media Posts will serve as notification to the United States Congress that should Iran strike any US person or target, the United States will quickly & fully strike back, & perhaps in a disproportionate manner," Trump wrote.

"Such legal notice is not required, but is given nevertheless!"

Responding to the tweet, the House Foreign Affairs Committee said: "This Media Post will serve as a reminder that war powers reside in the Congress under the United States Constitution. And that you should read the War Powers Act. And that you’re not a dictator."

While previous administrations have tried to garner bipartisan support for significant military operations by briefing opponents beforehand, neither Pelosi nor the top Democrat in the Senate, Chuck Schumer, were told in advance about the targeting of Soleimani.

A furious Pelosi said that what she called "this initiation of hostilities" was taken "without the consultation of the Congress and without the articulation of a clear and legitimate strategy to either the Congress or the public".

"As Speaker of the House, I reiterate my call on the administration for an immediate, comprehensive briefing of the full Congress on military engagement related to Iran and next steps under consideration," she said in a statement.

Speaking on ABC television, Schumer said he was worried that the president would drag the US into "what he (Trump) calls another endless war in the Middle East".

"I am really worried, and that is why Congress must assert itself. I don't believe the president has authority to go to war" in Iran without congressional approval, he added.

Secretary of State Mike Pompeo said the administration had begun to brief congressional leaders about the justification for the strike and promised to "keep them fully apprised".

Asked whether the administration would seek authorisation for any new military action, he told ABC television: "We have all the authority we need to do what we've done to-date. We will continue to do things appropriately, lawfully, and constitutionally."

Trump stands by threat to go after Iranian cultural sites

Trump on Sunday stood by his threat to go after Iranian cultural sites, warning of a "major retaliation" if Iran strikes back for the killing of one of its top military commanders.

The president, speaking to reporters on Air Force One, also threatened sanctions against US ally Iraq after its parliament called on American troops to leave the country.

Trump and his advisers have been defending the US drone strike that killed Soleimani, whose death has escalated tensions in the region. Trump says Soleimani was planning attacks against Americans and said he would consider releasing intelligence reports that led him to direct the killing.

Asked about potential retaliation by Iran, Trump said: "If it happens, it happens. If they do anything, there will be major retaliation."

Trump has said the operation was conducted to avoid war with Tehran and warned against further escalation, but he has employed tough rhetoric in public, tweeting that the United States had targeted 52 Iranian sites, some "at a very high level & important to Iran & the Iranian culture" if Iran struck any American or American assets in retaliation.

US Secretary of State Mike Pompeo denied on Sunday that Trump said he would target Iranian cultural sites, but the president contradicted him when asked about the issue on Sunday night.

"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," he said.

Targeting cultural sites with military action is considered a war crime under international law, including a UN Security Council resolution supported by the Trump administration in 2017 and the 1954 Hague Convention for the Protection of Cultural Property.

Sanctions threat to Iraq

The president also issued a threat to Baghdad after the Iraqi parliament's call for US and other foreign troops to leave the country in a backlash against the killing of Soleimani.

"We have a very extraordinarily expensive air base that's there. It cost billions of dollars to build, long before my time. Were not leaving unless they pay us back for it," Trump told reporters.

Trump said that if Iraq asked US forces to leave and it was not done on a friendly basis, "we will charge them sanctions like they've never seen before ever. It'll make Iranian sanctions look somewhat tame".