The future of the US military presence in Iraq is in question amid scenes of confusion in Washington, as the Trump administration scrambled to respond to Iraqi demands for the troops to leave after last week’s assassination in Baghdad of Iran’s top general, Qassem Suleimani.

The US-led coalition taskforce fighting Isis in Iraq delivered a letter to the Iraqi defence ministry on Monday saying preparations would begin right away “to ensure that movement out of Iraq is conducted in a safe and efficient manner”.

But soon afterwards, the defence secretary, Mark Esper, told journalists in the Pentagon: “That letter is inconsistent with where we are right now” and insisted that no decision had been taken to evacuate Iraq. The chairman of the joint chiefs of staff, Gen Mark Milley, said the letter had been sent in error.

“That letter is a draft, it was a mistake, it was unsigned, it should not have been released,” Milley said, adding that it was “poorly worded, implies withdrawal, that is not what’s happening”.

The withdrawal of the taskforce from Iraq would dramatically weaken the effort to stop Isis regrouping, marking a strategic victory for Iran and a serious setback for the Trump administration, which urged Baghdad not to expel its counter-terrorist forces.

The evident confusion in Washington added to an impression among US allies and enemies alike that the decision to assassinate Suleimani without a clear plan of what to do next had weakened the US in the region.

US allies have continued to distance themselves from the decision, as millions of Iranians took to the streets to mourn and demand revenge for the assassination of the country’s top general.

Both Israel and Nato stressed they were not involved in the airstrike on Thursday. The US secretary of state, Mike Pompeo, has already expressed disappointment in the lukewarm reaction of Washington’s European allies.

But the response of Israel’s prime minister, Benjamin Netanyahu, was particularly striking, as he has been one of Trump’s staunchest supporters on the world stage.

He told a meeting of his security cabinet on Monday: “The assassination of Suleimani isn’t an Israeli event but an American event. We were not involved and should not be dragged into it.”

The Saudi deputy defence minister, Khalid bin Salman, was in Washington on Monday to urge restraint, joining a growing international chorus.

France’s foreign minister, Jean-Yves Le Drian, insisted there was still time for diplomacy but warned that without urgent action to defuse rising tensions there was a real risk of a new Middle East war.

The UN secretary general, António Guterres, who spoke to Pompeo on Monday, said that the region’s “cauldron of tensions is leading more and more countries to take unpredicted decisions with unpredictable consequences and a profound risk of miscalculation”.

The Trump administration refused a visa to the Iranian foreign minister, Mohammad Javad Zarif, to come to New York to address the UN security council on Thursday, violating the UN headquarters agreement, the Foreign Policy website reported. A spokesman for the Iranian mission said it had not been informed of any decision, and a UN spokesman declined to comment.

The US letter to the Iraqi military was signed by the US commanding general in Iraq, Brig Gen William Seely, and said that US forces “will be repositioning over the coming days and weeks to prepare for onward movement”.

The taskforce would try keep disruption to a minimum and do much of the airlift at night “to alleviate any perception” that the US was bringing more troops into Baghdad’s fortified Green Zone.

In London, the foreign office would not confirm or deny reports that the UK was scaling back staff at its embassies in Iran and Iraq to a minimum level, saying only that both sites were open and “the safety and security of our staff is of paramount importance and we keep our security posture under regular review”.

Iran has threatened a severe response to the US killing of Suleimani by drone strike in Baghdad last week. Brig Gen Amir Ali Hajizadeh, the commander of Iran’s aerospace division, said on Monday that the only appropriate response would be the “the complete destruction of America in the region”.

While beginning to withdraw counter-Isis forces from Iraq, the Pentagon, meanwhile, continued to pour reinforcements into the region in case of a direct conflict with Iran. US defence officials said the roughly 2,500-strong marine force onboard the Bataan amphibious ready group, equipped with Cobra helicopters and Harrier jets, would be sent to the Middle East from its current position in the Mediterranean.

Three thousand airborne troops are already on the way to Kuwait, and CNN reported that B-52 bombers were being sent to the Indian Ocean base of Diego Garcia, for potential use over the Middle East.

On Monday, Iraq’s caretaker prime minister, Adil Abdul-Mahdi, had summoned the US ambassador, Matthew Tueller, and called on the two countries to cooperate in arranging the US withdrawal. However, Abdul-Mahdi did not give a deadline for the US departure.

Trump faced condemnation on Monday for his threat to strike Iranian culture sites among 52 targets that the US would bomb in reprisal for any future Iranian attack. The number, he explained, was the same as the number of Americans taken hostage when the US embassy in Tehran was seized after the Islamic revolution in 1979.

Trump was also under continued pressure from Democrats on Monday for the lack of transparency over his justification for the assassination of Suleimani, who commanded the elite Quds force of Iran’s Revolutionary Guards. Trump and Pompeo have claimed the general was plotting imminent attacks against US targets.

Abdul-Mahdi said the Iranian military leader had flown to Iraq to negotiate, and he claimed Trump had asked the Iraqi government to mediate.

Trump did not consult Congress or US allies before ordering the strike in the early hours of the morning in Baghdad. On Saturday, the White House delivered a formal notification to Congress as required by the 1973 War Powers Act, but its contents were classified. Normally such notifications are public documents with a classified section if required.

The Democratic senators Chuck Schumer and Bob Menendez wrote to Trump on Monday, demanding the war powers notification be declassified.

“We did not see anything here that he deemed required such a classification,” a Senate staffer said. “The War Powers Act provision requiring the 48-hour notification was included partly for transparency purposes with the American people during these delicate moments. [It’s] pretty self-defeating to hide something meant to be transparent.”

The White House has suggested it will brief selected members of Congress this week, but Kellyanne Conway, a Trump adviser, said the decision on timing was up to the Pentagon.

US allies in Europe and the Middle East have stressed that Suleimani had been a destabilising and destructive presence in the region, but they have largely stopped short of supporting Trump’s decision, calling for restraint on all sides.

The US briefed Nato ministers on Monday on the Suleimani killing. Speaking to journalists later, the Nato secretary general, Jens Stoltenberg, distanced the alliance from the operation.

“This is a US decision, it is not a decision taken by either the global coalition nor Nato, but all allies are concerned about Iran’s destabilizing activities in the region, Iran’s support to different terrorist groups,” Stoltenberg said. He also confirmed the suspension of the Nato training mission in Iraq.

“In everything that we do, the safety of our personnel is paramount. As such, we have temporarily suspended our training on the ground,” the secretary general said.

There is mounting concern that the more cautious stance by the US-led coalition would make it much less effective and allow Isis to regenerate.

“The bottom line is that there won’t be much counter-terrorism going on in Iraq and Syria any time soon,” wrote Luke Hartig, former senior director for counter-terrorism on the national security council, now at the New America foundation. “Trump’s counter-terrorism legacy in Iraq and Syria may be a series of dead bodies but nothing that addresses the core of the problem and no partners willing to help us root it out.”