WASHINGTON - US President Donald Trump threatened “major retaliation” on Sunday if Iran avenges the killing of a key military commander and he warned of massive economic sanctions against ally Iraq if the country expels US troops based there.

The twin threats came as Iran announced it was further reducing compliance with a tattered international nuclear accord, ending limitations on numbers of centrifuges used to enrich uranium.

The latest blow to the accord, which was meant to ensure Iran did not develop a nuclear weapon under cover of its nuclear industry, deepened the regional crisis set off by Friday’s killing of Iranian general Qasem Soleimani in Baghdad.

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 vacation in Florida.

Trump had already threatened bombing of 52 unspecified targets in Iran if Tehran attacks US troops and interests in the region. 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 neighboring 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.

In Baghdad, unidentified attackers launched a pair of rockets on 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 group Daesh in the region. If the government agreed, that would effectively require the departure of US soldiers supporting the local troops in the anti-Daesh 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. “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.”

Trump also thumbed his nose 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.

Two Democratic lawmakers 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!”

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.