President Trump criticized British Prime Minister Theresa May's handling of Brexit Thursday, telling The Sun newspaper that her plan was "very unfortunate" and would "probably" kill any possible trade deal between the U.S. and the U.K.

The comments could be seen as a body blow to May's government, which is struggling to steady itself after two key Cabinet members -- including Foreign Secretary Boris Johnson -- resigned in protest earlier this week at her plan to keep Britain and the European Union in a free market for goods, with a more distant relationship for services.

When asked about the ongoing negotiations between May's government and the EU over the terms of their divorce, Trump told The Sun: "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. I would actually say that she probably went the opposite way. And that is fine, she should negotiate the best way she knows how. But it is too bad what is going on."

May, who voted "Remain" in the 2016 referendum on leaving the EU, proposed earlier Thursday that Britain and the bloc would stick to a "common rulebook" with the EU for goods and agricultural products in return for free trade, without tariffs or border customs checks. Such a resolution would avoid disruption to automakers and other manufacturers that source parts from multiple countries.

The plan has enraged so-called "Brexiteers," who have looked to a possible U.S.-U.K. trade deal as one of the biggest boons that would result from leaving the 27-member bloc.

But Trump threw cold water on that prospect in his Sun interview, saying: "If they do a deal like [May's plan], we would be dealing with the European Union instead of dealing with the U.K., so it will probably kill the deal ... We have enough difficulty with the European Union. We are cracking down right now on the European Union because they have not treated the United States fairly on trading."

Trump even went so far as to question whether May's plan constituted a true exit from the European Union: "The deal she is striking is a much ­different deal than the one the people voted on. It was not the deal that was in the referendum."

In response to the interview, White House press secretary Sarah Sanders said in a statement that Trump "likes and respects Prime Minister May very much. As he said in his interview with the Sun she 'is a very good person' and he 'never said anything bad about her'. He thought she was great on NATO today and is a really terrific person.

"He is thankful for the wonderful welcome from the Prime Minister here in the U.K."

While Trump was critical of May, he was full of praise for Johnson, who he called "a very talented guy."

"I was very saddened to see he was leaving government and I hope he goes back in at some point. I think he is a great representative for your country."

When asked if Johnson could replace May as prime minister, Trump said: "Well, I am not pitting one against the other. I am just saying I think he would be a great Prime Minister. I think he's got what it takes."

Johnson, a former mayor of London, was the most prominent supporter of Brexit and resigned as foreign secretary after reportedly calling May's plan a "turd." Johnson was slightly more diplomatic in his resignation letter, warning May that Britain was "headed for the status of a colony" within the EU.

Trump also had harsh words for current London Mayor Sadiq Khan, a fervent critic of the president, saying Khan "has done a terrible job" running Europe's third-largest city.

"I think he has done a very bad job on terrorism. I think he has done a bad job on crime, if you look, all of the horrible things going on there, with all of the crime that is being brought in."

The president also warned that Britain and Europe was "losing its culture" due to mass migration.

"I think it changed the fabric of Europe and, unless you act very quickly, it’s never going to be what it was and I don’t mean that in a positive way."

The interview was published online as May greeted Trump at a lavish welcome reception at Blenheim Palace, the birthplace of Winston Churchill. Trump's staff has opted to keep him largely out of central London and the swarms of demonstrators who are expected to protest the president's every move during his two-day stay in the U.K.

Fox News' Serafin Gomez and The Associated Press contributed to this report.