UK MPs have attacked Donald Trump's sharing of far-right posts, accusing him of fuelling hate and calling for a planned state visit to be cancelled.
One Tory MP said the world would be "a better place" if Prime Minister Theresa May could persuade the US president to delete his Twitter account.
The US president retweeted three videos posted by a British far-right group.
When Mrs May said he had been "wrong" to do so he said she should focus on combating terrorism in the UK.
Home Secretary Amber Rudd said she hoped Mrs May's criticism "would have some impact on the president" – but she rejected calls for his state visit to be called off.
She said an invitation "has been extended and accepted" but the "dates and the precise timings have yet to be decided".
She urged critics of the president to remember the importance of the transatlantic alliance to Britain, saying intelligence sharing between the two countries had "undoubtedly saved British lives".
"That is the big picture here, and I would urge people to remember that," she added.
But she repeated Downing Street's condemnation of the US president, saying he had been "wrong" to share the posts by far-right group Britain First.
She said the UK government would "not tolerate any groups who spread hate by demonising those of other faiths or ethnicities".
Responding to a call by MP Peter Bone for the president to delete his account, she said: "It's interesting to note [Mr Bone's] advice regarding Twitter accounts – I'm sure many of us might share his view."
Former Conservative minister Tim Loughton said if Twitter was "genuine in its commitment to fight hate crime online" it would delete the US president's account.
Ms Rudd replied: "I am sure that the chief executive of Twitter will have heard the interesting suggestions from (Mr Loughton) and we will leave it to them to decide what action to take."
Several MPs called for the state visit to be cancelled, with former Labour cabinet minister Yvette Cooper saying Britain could not "simply roll out a red carpet and give a platform for the President of the United States" to "sow discord in our communities".
Veteran Labour MP Paul Flynn said if Mr Trump should be "charged with inciting racial hatred" if he comes to the UK, a view echoed by fellow Labour MP Naz Shah.
Mr Trump earlier hit back at Downing Street's criticism of his tweets, saying: "Don't focus on me, focus on the destructive radical Islamic terrorism that is taking place within the United Kingdom."
An unnecessary controversy
By Anthony Zurcher, North America reporter
It's clear at this point that Donald Trump won't let a perceived slight or criticism go unanswered – even if it's from a supposed friend. Even if it's from the leader of the president's closest international ally.
So shock isn't exactly the right word to describe the reaction to Mr Trump's initially botched attempt to tell Theresa May to, in effect, mind her own business. This is just another example of the US president's self-described "modern-day presidential" use of social media, where Twitter is a cudgel for score-settling no matter the diplomatic cost.
When Mr Trump assumed the presidency, one of the first foreign dignitaries he received was Mrs May, and it appeared they formed a quick bond – briefly holding hands as they walked past the White House Rose Garden. Those bonds will now be tested in a spat over a few morning retweets of inflammatory videos.
It's a wholly unnecessary controversy, but the international consequences could be all too real.
The US and the UK are close allies and often described as having a "special relationship". Theresa May was the first foreign leader to visit the Trump White House.
The videos shared by Mr Trump, who has more than 40 million followers, were initially posted by Jayda Fransen, the deputy leader of Britain First, a group founded by former members of the far-right British National Party (BNP).
Ms Fransen, 31, has been charged in the UK with using "threatening, abusive or insulting words or behaviour" over speeches she made at a rally in Belfast.
Several leading UK politicians have criticised the president for retweeting her posts, as has the Archbishop of Canterbury Justin Welby, who said it was "deeply disturbing" that Mr Trump had "chosen to amplify the voice of far-right extremists".
Communities Secretary Sajid Javid said Mr Trump had "endorsed the views of a vile, hate-filled racist organisation that hates me and people like me", adding: "He is wrong and I refuse to let it go and say nothing."
London Mayor Sadiq Khan repeated his call the state visit to be cancelled, saying: "It beggars belief that the president of our closest ally doesn't see that his support of this extremist group actively undermines the values of tolerance and diversity that makes Britain so great."
In hitting out at Mrs May, Mr Trump first tagged the wrong Twitter account, sending his statement to a different user with just six followers. He then deleted the tweet and posted it again, this time directing the message to the UK PM's official account.
After already condemning Mr Trump's actions on Wednesday, Brendan Cox – whose wife, MP Jo Cox, was murdered by a right-wing extremist who shouted "Britain first" before committing the act – told the US president to focus on problems in his own country.
You have a mass shooting every single day in your country, your murder rate is many times that of the UK, your healthcare system is a disgrace, you can’t pass anything through a congress that you control. I would focus on that. https://t.co/SNcqOZGvLQ
— Brendan Cox (@MrBrendanCox) November 30, 2017
End of Twitter post by @MrBrendanCox
What did Trump retweet?
The first video purportedly shows a "Muslim migrant" attacking a young Dutch man on crutches. However, the claim in this tweet appears to have little substance.
A spokesperson from the Dutch Public Prosecution Service told the BBC that the person arrested for the attack "was born and raised in the Netherlands" and was not a migrant.
The Dutch embassy in Washington DC confirmed this on Twitter.
The second video retweeted by Mr Trump shows a man smashing a statue of the Virgin Mary.
This video was uploaded to YouTube in 2013. The man in the clip says: "No-one but Allah will be worshipped in the land of the Levant," which could place him in Syria.
The third video originates from the riots that took place in Egypt in 2013, and shows a man being pushed from the top of a building in Alexandria. In 2015, those involved in the incident were prosecuted, and one man was executed.
White House spokeswoman Sarah Sanders said on Wednesday that Mrs May and other world leaders knew that "these are real threats that we have to talk about".
"Whether it's a real video, the threat is real," she said.
What other reaction has there been?
Mr Trump's actions on Wednesday were criticised by both Democrats and Republicans.
Republican Senator John McCain said he was "surprised" at the president's tweets.
Meanwhile, Senator Orrin Hatch of Utah said that Mrs May was "one of the great world leaders", adding that he had "incredible love and respect for her".
Khizr Khan, the father of US soldier Humayun Khan who was killed in the Iraq war, told Today: "[Mr Trump] holds the hatred. He is an actor, he acts and fabricates these facts to exploit people, innocent people, that fall victim to his bigotry and he sees the benefit.
"We all need to unite ourselves, all decent people of the world, against the menace of terrorism."
So POTUS has endorsed the views of a vile, hate-filled racist organisation that hates me and people like me. He is wrong and I refuse to let it go and say nothing
— Sajid Javid (@sajidjavid) November 29, 2017
End of Twitter post by @sajidjavid
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