(CBS)–President Trump said U.K. Prime Minister Theresa May is “doing a fantastic job” as British prime minister, and even said he apologized to her Friday morning before their meeting, after an interview published Thursday highlighted his criticism of her handling of Brexit.

AYLESBURY, ENGLAND – JULY 13: Prime Minister Theresa May walks with U.S. President Donald Trump at Chequers on July 13, 2018 in Aylesbury, England.  (Photo by Jack Taylor/Getty Images)

“I think she’s a terrific woman,” he told reporters at a joint press conference Friday at the country estate of the prime minister, Chequers. The president also called the relationship between the U.S. and U.K. the “highest level of special.” But Mr. Trump still thinks, as he told The Sun tabloid, that May’s Conservative Party rival Boris Johnson would be a great prime minister.

According to Mr. Trump, he also did not criticize May and that reports to the contrary were “fake news.”

“I didn’t criticize the PM. I have a lot of respect for the PM. And unfortunately there was a story that was done, which was generally fine, but it didn’t put in what I said about the PM,” he said.

Mr. Trump’s visit to Britain is sandwiched between the Brussels NATO summit, where he blasted allies over defense spending and trade, and ahead of his meeting with Russian President Vladimir Putin in Helsinki, Finland. Mr. Trump promised to take a firm line with Putin and tell him to stop interfering in U.S. elections.

On Friday, Mr. Trump met and dined with May, who faces her own political challenges, with just days to come up with a new plan for Brexit or face a vote of no confidence in parliament. Two top U.K. officials overseeing Brexit negotiations, including Johnson, resigned from her government earlier this week.

Reporters questioned Mr. Trump about his commitment to NATO, given his recent criticisms of the organization, and about his upcoming meeting with Putin.

On the day before the news conference, the British tabloid The Sun published an interview with Mr. Trump in he said Johnson would make a great prime minister, and Britain’s trade relationship with the U.S. could face turbulence if May follows through with what’s known as the so-called “soft” Brexit blueprint. The president made the comments ahead of meetings with May and Queen Elizabeth.

May’s “soft” Brexit plan would keep strong economic ties with the European Union. Mr. Trump said he advised May how to manage Brexit, but she didn’t listen.

“I did give, Theresa, who I like — I did give her my views on what she should do and how she should negotiate, and she didn’t follow those views,” Mr. Trump told the Sun. “I would actually say she probably went the opposite way.”

AYLESBURY, ENGLAND – JULY 13: Prime Minister Theresa May and U.S. President Donald Trump make their way to a joint press conference following their meeting at Chequers on July 13, 2018 in Aylesbury, England. Photo by Stefan Rousseau-WPA Pool/Getty Images)

Here’s a rundown of the Friday press conference: 

“The highest level of special”

Mr. Trump characterized the relationship with the U.K. as “the highest level of special.”

He then tried to call on Fox News’ John Roberts, as CNN tried to ask a question. Mr. Trump said he didn’t take questions from “fake news” CNN.

Roberts asked about the relationship with Putin and the ongoing investigation into Russian meddling in the election. Mr. Trump said after watching Peter Strzok that was testifying yesterday, the investigation is a “rigged witch hunt.”

He also acknowledged Russia’s occupation of Crimea, but the president blamed President Obama for allowing Putin into Crimea in the first place. He said of Putin, “I don’t think he would have done that with me.”

“We’ll see what happens,” Mr. Trump said. “It’s another bad hand,” he said again of inheriting the annexation of Crimea. I’m fixing them one by one, he said of the other “bad hands” from the Obama presidency.

May said that what’s important in meeting with President Putin is the position of strength and unity with NATO.

Boris Johnson as prime minister, Brexit

May did not answer a question related to the president’s remark to the Sun that Johnson would be a good prime minister. She did reiterate on Brexit, “We will be leaving the European Union.”

On the 29 of March, 2019, there will be an end to free movement, end to sending vast amounts of money to the E.U., she promised.

“That’s what the British people voted for and that’s what we will be delivering,” May insisted.

Mr. Trump praised Johnson and said again that he would be a great prime minister. But he also said that May is doing a “fantastic” job as prime minister.

She’s going to do the “best,” he said. Mr. Trump said he only asked for an “even” deal with the U.K. He complained about E.U. trade barriers and tariffs on cars. He said that the U.S. lost $151 billion to the E.U.

Impact of immigration

Mr. Trump said, “I think it’s changing the culture.” He also added that he has a great relationship with Angela Merkel, but I think it’s “hurt Germany.”

I think they better watch themselves, he said. Countries that never had difficulties — I don’t think it’s good for Europe, and I don’t think it’s good for our country, Mr. Trump said of immigration.

May said that the U.K. has a proud history of welcoming immigrants to the U.K., but she said that border control was important

Putin meeting, NATO

Asked what he hopes to accomplish in meeting Monday with Vladimir Putin, the president touted the “strong” meeting with NATO. He said the two would be talking about Ukraine, Syria, other parts of the Middle East, nuclear proliferation. It’s a “devastating technology,” he said. It’s a “bad policy.” We have no choice. We are massively big and they are very big, Mr. Trump said.

He promised to bring up Russian meddling in the 2016 election, and said he’d “firmly” ask the question, though he expressed doubt that Putin would make any admissions. He also suggested that the special counsel’s investigation into Russian meddling in the election is an obstacle to his relationship with Putin.

He also addressed NATO – “they’re now paying their way,” he said of the other member states.

“We have been very strong on Russia,” the president said in response to another question about NATO and Russia. If we get along with other countries, that’s a good thing, Mr. Trump said. He stressed the increased contributions of other NATO countries and said Putin wouldn’t like this development.

Mr. Trump said that he’s not going into the meeting with Putin with high expectations, but having a relationship with Russia and other countries is “really a good thing.”

He also mentioned that nuclear weapons are the “biggest problem in the world,” he said. Ideally he’d “get rid of them,” he mused. Mr. Trump said he would talk about nuclear proliferation is a subject he said he would bring up with Putin

Trump asked about Sun interview

“I have a lot of respect for the prime minister,” Mr. Trump said in response to a question about the Sun interview. It’s “fake news,” he said.

He said the U.S. is by far the biggest trading partner of the U.K. He said that the trade is “a little bit tricky,” but said he believes a deal will happen.

May said the Brexit deal announced at Chequers fulfills the promise of the British exit. We will have an independent trade policy, she said. And she said the U.K. would do a trade deal with the U.S. and others around the world.

Mr. Trump said near the end of the news conference, “I said very good things” about Theresa May. He wondered if those comments had only made it onto the internet. He said he apologized to May for the article, and she responded, ‘Don’t worry, it’s only the press.’

Trump opening remarks

The president said that the two leaders had come from a “productive” NATO summit where he had insisted that other leaders pay their fair share of defense spending and honor their commitments and do so “in a much more timely manner.”

He thanked May for support in pushing for a nuclear-free North Korea.

He mentioned he hoped to find a couple of Democratic votes on immigration policy.

U.S. looks forward to finalizing bilateral trade agreement with the U.K., Mr. Trump said. A strong and independent U.K. is truly a blessing on the world, he said.

He said the two had had a wonderful visit — we just talked about a lot of different problems and solutions to those problems, he said of their dinner last night

News conference begins – May speaks

May said the partnership between U.S. and U.K. is growing. She said the two leaders will pursue an “ambitious” trade deal, reducing tariffs, creating new jobs and prosperity.

May referred to the importance of “making tough calls” and saying things others might not want to hear.

She praised efforts to deal with the North Korean nuclear threat, destabilizing influence of Iran in the Middle East, insisting on increasing NATO spending levels by allies.

It is all of our responsibility to ensure that transatlantic unity endures, May said. I’m confident that this transatlantic alliance will be bedrock of our shared prosperity for years to come, she said

Trump and May meet before news conference

The president and May met before the press conference at the prime minister’s country residence Chequers, and in a photo opportunity with reporters, Mr. Trump said that they had worked hard together at the NATO summit this week and declared that NATO has never been more united. He also mentioned that the U.S. and U.K. are two countries who have met NATO spending levels.

The two leaders did not address his comments to the Sun during the photo op, though a pool reporter asked about the interview.

“The relationship is very strong,” Trump said. He also said they “probably never developed a better relationship than last night,” during their dinner at Blenheim Palace, the birthplace of Winston Churchill.