Refugees and passengers from a number of countries detained at airports but Theresa May refuses to condemn move

Donald Trump’s decision to ban immigration from a string of Muslim-majority nations has sparked fury and anguish around the world as refugees and migrants were prevented from boarding flights to the US.

Holders of passports from Iran, Iraq, Libya, Somalia, Sudan, Syria and Yemen were stopped at airports, while passengers already in the air were detained in the US. In one incident, five Iraqi passengers and one Yemeni, all holding valid visas, were barred from boarding an EgyptAir flight from Cairo to New York and instead redirected on to flights to their home countries.

A Yazidi woman, who fled an Isis massacre in Iraq in 2014, was stopped from boarding a flight in Baghdad, after waiting months for a visa to be reunited with her husband, who is already in the US.

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President Trump has imposed a three-month ban on refugees from the seven countries, claiming that the “extreme vetting” order would “keep radical Islamic terrorists out of the US”. Refugees from Syria are banned indefinitely.

A homeland security spokesman said on Saturday night that green card holders – in effect, permanent residents – will also be covered by the ban, while a senior White House official indicated it was likely to be extended to other countries. A state department spokesman confirmed that travellers from the named countries who have dual nationality will not be able to enter the US for 90 days. Members of religious minorities from those countries will, however, be granted immigration priority.

Trump said that the initial implementation of the plan was working well. “It’s not a Muslim ban,” he told reporters in the Oval Office at the White House. “It’s working out very nicely. You see it at the airports, you see it all over. We’re going to have a very, very strict ban and we’re going to have extreme vetting, which we should have had in this country for many years.”

As the global backlash developed, Britain’s prime minister, Theresa May, refused to condemn the ban. On Saturday night, after she landed back in Britain, a Downing Street source said: “We will always find ourselves in agreement on some things and disagreement on other things.”

Earlier, during a visit to Ankara to meet her Turkish counterpart, Recep Tayyip Erdoğan, she said the US was responsible for its own refugee policy. But other politicians voiced dismay, including May’s host, who condemned a “closed door” attitude. “You can’t solve these problems by building walls,” said Erdoğan. “Nobody leaves their homes for nothing. Our doors are open, and if the same thing happens again, we would do the same thing again.”

Facebook Twitter Pinterest German foreign minister Sigmar Gabriel reminded Trump that ‘welcoming refugees fleeing war and oppression forms part of our duties’. Photograph: Kay Nietfeld/AP

The Tory MP Nadhim Zahawi tweeted: “Had confirmation that the order does apply to myself and my wife as we were both born in Iraq. Even if we are not dual nat. I’m a British citizen and so proud to have been welcomed to this country. Sad to hear I’ll be banned from the USA based on my country of birth.”

The storm over the ban cast a shadow over May’s Washington trip, which had initially been widely deemed a success. But a growing number of leading Tory MPs joined in the condemnation of the policy.

Sarah Wollaston, chair of the Commons health select committee, said Trump must not be invited to address both Houses of Parliament from Westminster Hall on his state visit later this year, pointedly insisting that “those who wish to fawn over him” should do so elsewhere. Scottish Tory leader Ruth Davidson said the ban was “both wrong in itself and very worrying for the future”.

Heidi Allen, MP for South Cambridgeshire, hit out on Twitter at the way May had handled the situation. “Strong leadership means not being afraid to tell someone powerful when they’re wrong. It’s an ethos this country is proud of #theresa-may. I don’t care how special the relationship is – some lines just shouldn’t be crossed.”

Jeremy Corbyn also attacked the PM for failing to condemn Trump’s actions. “President Trump’s executive order against refugees and Muslims should shock and appal us all. Theresa May should have stood up for Britain and our values by condemning his actions. It should sadden our country that she chose not to.

“After Trump’s hideous actions and May’s weak failure to condemn them, it’s more important than ever for us to say to refugees seeking a place of safety that they will always be welcome in Britain.”

It emerged on Saturday night that the Iranian director Asghar Farhadi, who was nominated in the best foreign film category for The Salesman, feared he will not be able to attend next month’s Academy Awards. Trita Parsi, president of the National Iranian American Council, tweeted on Saturday morning that Farhadi would indeed be banned.

On Saturday night, Iran announced that it would take reciprocal measures in retaliation. Without directly naming the US, President Hassan Rouhani said on state television: “Today is not the time to erect walls between nations. They have forgotten that the Berlin Wall fell years ago.”

The temporary ban is expected to be the subject of myriad legal challenges. The first arrived on Saturday lunchtime, as lawyers representing two Iraqi refugees held at JFK airport in New York argued that their clients had been unlawfully detained. The American Civil Liberties Union is also involved in the lawsuit. Other class actions on behalf of excluded refugees are expected to be filed.

Germany’s foreign minister, Sigmar Gabriel, and former French prime minister Jean-Marc Ayrault, issued a statement reminding the US president that international obligations meant that “welcoming refugees fleeing war and oppression forms part of our duties”.

Canadian prime minister Justin Trudeau tweeted: “To those fleeing persecution, terror and war, Canadians will welcome you, regardless of your faith. Diversity is our strength #WelcomeToCanada.”

In the US, there was horror and incredulity among groups that work with refugees and migrants. Thanu Yakupitiyage, a spokeswoman for the New York Immigration Coalition, told the Observer: “This is dehumanising. I am livid. It’s outrageous. People are in a state of shock.”

Immigration policy analyst David Bier, from the Cato Institute’s Center for Global Liberty and Prosperity, described Trump’s order as “illegal” as it appeared to target a religious group. The Council on American-Islamic Relations said it would issue a court challenge on Monday, claiming that the new entry rules target Muslims because of their faith and therefore contravene the constitutional right to freedom of religion.

Former British foreign secretary David Miliband, now president of the International Rescue Committee, said the suspension of the refugee resettlement programme was a “harmful and hasty” decision. “America must remain true to its core values. It must remain a beacon of hope,” he said. He added that the vetting process was already robust, involving biometric screening and up to 36 months of investigations by 15 agencies.

New York’s International Refugee Assistance Project (IRAP) said the extreme vetting order meant the US would no longer be able to lead by example in matters of global humanitarian concern.

Syrian refugees in Jordan lamented the policy change. Ammar Sawan, 40, who began his first step toward US resettlement three months ago, said: “It was like a bolt of lightning. All our hopes and dreams vanished.” In Britain, Ibrahim Mogra, chair of the Christian Muslim Forum, said Trump’s action suggested he viewed Muslims as “subhuman”.

Yvette Cooper MP wrote to May saying she hoped the prime minister was “aware of the dangerous implications and the humanitarian consequences of the US – a country built on giving sanctuary – taking this decision now”.