Responding to Mr Trump's comments about The Sun, a spokesman for the newspaper said: "We stand by our reporting and the quotes we used - including those where the president was positive about the prime minister, in both the paper and in our audio - and we're delighted that the president essentially retracted his original charge against the paper later in the press conference".
Mrs May will host Mr Trump and his wife Melania at a lavish dinner at Blenheim Palace on Thursday evening.
Sterling came under pressure on Friday following comments by Donald Trump that a post-Brexit trade deal between Britain and the USA could be dead. That's your decision, just make sure we can trade together that's all that matters.
British tabloid newspaper The Sun published an interview with Trump on Thursday, where the president blasted May's Brexit negotiations, as well as European immigration policy, North Atlantic Treaty Organisation and London Mayor Sadiq Khan.
"I would have done it much differently", he told The Sun, which urged its readers to back Brexit before a referendum in June 2016. And that's fine. She should negotiate the best way she knows how.
Khan approved a request for a giant blimp depicting Trump as an orange baby to fly over London during protests on Friday.
The president started the day by reviewing a private military exercise alongside May at the Royal Military Academy Sandhurst.
"I guess when they put out blimps to make me feel unwelcome, no reason for me to go to London", he said.
Emmett Till Murder Investigation Reopened Due to 'New Information'
Though a judge ruled Carolyn's testimony inadmissible in court, her husband and Milam were quickly acquitted. He says he assumes his book helped prompt the renewed investigation of the black teen's brutal slaying.
A high metal fence has been erected around the USA ambassador's central London residence where Trump will spend Thursday night and the embassy has sent out an alert warning Americans in London to keep a low profile in case protests turn violent.
After a North Atlantic Treaty Organisation summit where he provoked a crisis session to force allies to raise their defence spending, Trump landed in Britain having described the closest U.S. ally in Europe as being in turmoil over Brexit. And Trump has now openly sided with them against the prime minister.
"Mr. President, Sir Winston Churchill once said that "to have the United States at our side was, to me, the greatest joy", May told Trump, according to a text of her speech.
"He would make a great prime minister", Trump told the tabloid.
If signing up to the Trump world view is the price of a deal, it's not worth paying", she tweeted, adding that Trump was "determined to insult" the prime minister."Our prime minister is so weak she still rolls out the red carpet for a man who does nothing but insult her.
Trump has also frequently angered British politicians and has been involved in social media spats with London's Muslim mayor Sadiq Khan who he said had "done a very bad job on terrorism". The president claimed Europe is "losing its culture" because of immigration from the Middle East and Africa.
Trump said he had made a suggestion to May on a negotiating tactic with Brussels that she had not taken because it was "maybe too brutal", but she could still use it if things took a turn for the worse.
At the time, Khan also said "Trump is not welcome here" in London.