LONDON — At a lengthy joint news conference Friday, President Donald Trump backed away from his harsh criticism of British Prime Minister Theresa May, said immigration has been a "very negative thing" in Europe and the United States, and argued that U.S. relations with Russia have been badly damaged by the ongoing special counsel investigation that he called a "rigged witch hunt."

"I didn't criticize the prime minister," Trump said. "It’s called fake news."

Trump's remarks came just hours after the British tabloid The Sun published an interview with him in which he torched May over her handling of the U.K.'s impending divorce from the European Union and, perhaps more important, said that if her plan for Brexit goes forward it would "probably end" the chances of a bilateral trade agreement between the U.S. and Britain. The Sun released a recording of the interview.

But with May standing at his side Friday, Trump praised her and said he wants to make a trade deal with Britain. The concern for May's critics has been that her proposal does too little to detach the U.K. from the European Union, a fear Trump played into in the Sun interview but played down at the news conference.

"She’s going to make a decision as to what she’s going to do," Trump said. "We want to trade with the U.K. and the U.K. wants to trade with us. ... I think she's doing a terrific job, by the way."

Earlier in the day, when asked directly whether he regretted the interview, which appeared at a time when May's job is on the line over her "soft" Brexit proposal, Trump closed his eyelids and rolled his eyes.

Later, the president had a quieter arrival at Windsor Palace, where Queen Elizabeth II greeted Trump and first lady Melania Trump in a courtyard as a red-coated military band played "The Star-Spangled Banner." Trump appeared to follow decorum by refraining from touching the monarch before heading inside with her for a private tea.

Meanwhile, at the same moment back in Washington, Deputy Attorney General Rod Rosenstein announced new indictments against 12 Russian operatives accused of hacking the Democratic National Committee and others to influence the 2016 election in Trump's favor.

Trump, who will meet with Russian President Vladimir Putin next week, has repeatedly cast doubt on Russia's involvement in the election, once again calling special counsel Robert Mueller's investigation a "rigged witch hunt" Friday morning at the news conference.

As a growing list of Democratic lawmakers called on the president to cancel the planned summit with the Russian leader, a senior administration official told NBC News there was a "zero" percent chance the sitdown would not take place. Later, White House Press Secretary Sarah Sanders said the summit was "still on."

May and Trump met at Chequers, the prime minister's country house, before he departed to Windsor Castle to sit down with Queen Elizabeth II. Trump's one-day, 180-degree turn on May and a U.S.-U.K. trade deal came right after he traveled a similar path at a two-day NATO summit in Brussels earlier in the week.

At that meeting, Trump pronounced the alliance unified and strong a day after leveling blistering criticism at Germany and other nations.

While Trump's interview with The Sun sent a shockwave through Britain's political class, his praise of May and willingness to engage in trade talks could go a long way toward softening the effect.

Today’s ⁦@EveningStandard⁩: after Trump slags off London, the NHS and immigrants to our shores we say ‘No, Mr President” pic.twitter.com/RlxPkIUdR3 — George Osborne (@George_Osborne) July 13, 2018

Matthew Doyle, who was a political adviser to Tony Blair, the British prime minister, predicted before the chummy news conference that Trump might change his tune in a way that helps May.

"Consequences are significant unless Theresa May can persuade her parliamentary colleagues that this is Bad Cop President Trump going into their meetings and Good Cop President Trump will emerge afterward," he said.

Still, Trump also repeated praise for Boris Johnson, who resigned this week as May's foreign minister and is seen as a power rival within her own Conservative Party.

"I said he'd be a great prime minister," Trump said. "He's been very nice to me. He's been saying very nice things about me as president. I think he thinks I'm doing a great job. I am doing a great job, that I can tell you, just in case you haven't noticed. Boris Johnson I think would be a great prime minister.”

The views Trump expressed in the interview reflect the line of argument made by critics like Johnson about her Brexit plan, which would keep the U.K.'s rules consistent with certain E.U. standards on the trade of goods.

In the interview, Trump insisted that he would have negotiated the deal differently than May, and he said that he had provided the prime minister his "views on what she should do and how she should negotiate."

"I would have done it much differently. I actually told Theresa May how to do it but she didn’t agree, she didn’t listen to me. She wanted to go a different route," he said.

But, without specifying his prescription, he took a softer approach Friday.

"I could fully understand why she thought it was a little bit tough," he said of the advice he offered, saying it had merely been a "suggestion."

His comments didn't occur in a vacuum.

Trump also expounded on his formulation that immigration has "changed the fabric" of Europe's culture and is bad both for Europe and the U.S.

"I think it's changing the culture, it's a very negative thing for Europe. I know it's politically not necessarily correct to say that, but I'll say it and I'll say it loud," he said. "I do not think it's good for Europe, and I don't think it's good for our country."

He also said the investigation into his 2016 campaign's ties to Russia is harmful to the U.S., particularly as he aims to form a better relationship with Putin when the two meet in Helsinki on Monday.

"I think that we're being hurt very badly by the — I would call it 'the witch hunt.' I would call it 'the rigged witch hunt,'" he said of Mueller's probe. "I think that really hurts our country and it really hurts our relationship with Russia. I think that we would have a chance to have a very good relationship with Russia."

Trump said "yes" when asked whether he would tell Putin not to meddle in American elections, and he said he planned to discuss nuclear nonproliferation, the war in Syria and other Middle East issues with Putin.