Trump is staying at one of his luxury golf resorts in Turnberry, southwest of Glasgow, in a private part of the trip before heading for a summit with Russian President Vladimir Putin in Helsinki.
Scottish First Minister Nicola Sturgeon, a fierce critic of Trump, has refused to meet him and he was instead met at Glasgow airport by a British government representative.
Bad blood over golf course stalks Trump's Scotland trip
A major anti-Trump rally is planned in Edinburgh on Saturday after a mass protest in London Friday that organisers said drew more than 250,000 people.
A pro-Trump demonstration is also due to be held in London by alt-right campaigners, as well as a counter, anti-fascism protest.
In an extraordinary interview with Friday's edition of The Sun tabloid, Britain's most widely read newspaper, Trump said May's plan for post-Brexit ties with the EU would "probably kill" prospects for a UK-US trade deal.
He also said former foreign minister Boris Johnson, who resigned over the plan earlier this week and is a potential challenger to May, would make "a great prime minister".
Trump said he had advised May to take a different strategy on Brexit, telling the paper: "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".
Tens of thousands march through London in anti-Trump protests
The unprecedented criticism comes at a particularly sensitive time for May, who is facing a rebellion by Brexit hardliners against her proposals to retain strong trading ties with the EU even after Britain leaves the bloc.
After meeting May at her Chequers country retreat outside London on Friday, Trump sounded more conciliatory, saying that bilateral relations "have never been stronger".
"Whatever you do is okay with us, just make sure we can trade together, that's all that matters," he told May.
"The United States looks forward to finalising a great bilateral trade deal," he said, and repeatedly praised May's leadership, saying she was a "terrific woman".
Trump is staying at the Turnberry golf resort -- the same course he inaugurated on June 24, 2016, a day after the referendum in which Britain voted to leave the EU.
Discord over his other golf course in Scotland dating back over a decade means there is little love lost between Trump and the pro-independence government in Scotland.
Trump blasts May's Brexit strategy on UK visit
In 2006, the billionaire real estate tycoon bought 1,400 acres of land near Aberdeen and promised to build "the world's best golf course".
The proposal was welcomed by the government at the time and Trump was named a "Global Scot" business ambassador.
But local councillors rejected the plan amid fierce opposition from conservationists and neighbouring residents.
The SNP government overturned the councillors' decision shortly after golf-loving nationalist Alex Salmond took control, kicking off a short and tempestuous bromance with Trump who called Salmond "an amazing man".
However, the relationship cooled when Trump's promise to create 6,000 jobs and invest £1 billion failed to materialise, and Trump began interfering with the SNP's flagship plan to make Scotland a renewable energy powerhouse.
The Trump Organisation has spent around £100 million on the course, known as Trump International Golf Links, and employed around 650 temporary and permanent staff -- but the company insists the resort remains a work in progress.
Three years later Trump visited the Scottish Parliament to complain about plans to build 11 "ugly" offshore wind turbines near his newly minted Aberdeenshire resort, insisting the development would do "terrible damage" to Scottish tourism.
Trump declared "I am the evidence" when Scottish lawmakers asked him to back up his assertion that the wind farm would "destroy the financial wellbeing of Scotland".
Sturgeon, who rescinded Trump's "Global Scot" title after he pledged to cut Muslim immigration into the United States, switched on the first wind turbine last week.
"A famous golf course owner from America who, I think, has now turned his hand to politics, decided to take the Scottish government to court to try to block these wind turbines," she told reporters.
"The Scottish government beat that American golf course owner in court... and these amazing wind turbines generated their first electricity," she said.
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