Theresa May was "very happy" to invite Donald Trump for a controversial state visit to the UK, Downing Street said amid widespread outrage at his travel ban.
Number 10 said the Prime Minister extended the invitation on behalf of the Queen and "we look forward to hosting the President later this year".
More than a million Britons have signed a petition against the state visit and there was confusion over impact Mr Trump's executive order will have on UK dual national citizens.
Read more: Donald Trump's UK state visit will go ahead despite one million backing petition
Foreign Secretary Boris Johnson said on Sunday that he had been assured by Mr Trump's team that Britons who have shared nationality with one of the seven mainly-Muslim countries covered by the restrictions would not be stopped from entering America.
But an urgent notice issued by the US Embassy in the UK on Monday appeared to contradict guidelines issued by the FCO stating that dual UK citizens "from one of the seven countries travelling to the US from outside those countries are not affected".
Whitehall sources said they expected the US mission's advice to be changed after the Foreign Office confirmed the position with the White House.
Number 10 had been under pressure to explain why the honour of a state visit had been extended to the President so soon after taking office.
The Prime Minister's spokesman said normal procedure was followed after recommendations were made by a committee for state visits which works within the Foreign Office.
Read more: Donald Trump's UK state visit will go ahead despite one million backing petition
"There is no set timing that a president needs to be in office before they receive, or don't receive, an invitation for a state visit.
"There is a process for state visits. Each year the Government looks at the recommendations that are made by the committee for state visits. Those recommendations are then put to Buckingham Palace, the Palace then needs to agree to the visit, then, historically, the invitation is extended on behalf of Her Majesty by the Government, and that is the process that took place this time," he said.
In a subsequent statement, Downing Street said: "To be clear, the Prime Minister extended an invitation on behalf of the Queen - and she was very happy to do so. The USA is one of this country's closest allies, and we look forward to hosting the President later this year."
Mr Trump remained unmoved by the worldwide condemnation of his move, responding with a tweet: "There is nothing nice about searching for terrorists before they can enter our country. This was a big part of my campaign. Study the world!"
Mr Johnson will face MPs to explain the chaotic situation around UK citizens who hold dual nationality with one of the countries covered by Mr Trump's order.
Read more: Donald Trump's UK state visit will go ahead despite one million backing petition
A statement on the US embassy's website said: "Urgent Notice: Per US Presidential Executive Order signed on January 27 2017, visa issuance to aliens from the countries of Iraq, Iran, Libya, Somalia, Sudan, Syria and Yemen has been suspended effective immediately until further notification.
"If you are a national, or dual national, of one of these countries, please do not schedule a visa appointment or pay any visa fees at this time.
"If you already have an appointment scheduled, please do not attend your appointment as we will not be able to proceed with your visa interview."
But a UK Government spokesman insisted the FCO guidance "was cleared by the top team in the White House and they are in charge".
A Government source said that after seeing the US Embassy guidance, Mr Johnson "sought clarity from the White House and was informed that the FCO statement was correct".
The Prime Minister's spokesman said Mrs May "disagreed" with the travel ban, but the planned state visit would not be affected by it, or the petition to Parliament calling for it to be downgraded.
Labour leader Jeremy Corbyn said: "It is outrageous. It is illegal as well as immoral. I think we should stand up for the values that we believe in; that is, we don't discriminate."
Asked whether the Government needed to look at the bigger picture, he told the BBC: "The bigger picture is peace, justice and human rights, the bigger picture is - of course - good trade arrangements. I don't think the two things are mutually exclusive."
Mr Corbyn said he would send a member of his team along to an anti-Trump protest in London later "and if I can I will be there".
London mayor Sadiq Khan, who is a Muslim, wrote in the Evening Standard: "We must now rescind the offer of a full state visit for President Trump - until this ban is lifted.
"I don't believe the people of London will support rolling out the red carpet until this happens."
Tory peer Baroness Warsi, who was the first female Muslim cabinet minister, said the US president should not be given the honour.
She told the BBC Radio 4 Today programme: "Those who run and govern this country bowing down to a man who holds the views that he holds, values which are not the same as British values, I think is sending out a very wrong signal."
Tory MP Sarah Wollaston has said Mr Trump must not be invited to address both Houses of Parliament from Westminster Hall, pointedly insisting "those who wish to fawn over him" should do so elsewhere.
Number 10 said it was too early to comment on whether Mr Trump would address Parliament or not during his visit.
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