The two are meeting in London, just days before May is to step down as party leader Friday, setting in motion a race to succeed her as prime minister.
The leaders' top priority is a possible bilateral trade deal to take effect once the U.K. leaves the European Union.
Before their meeting with business leaders, May says the two nations' business relationship can be enlarged and a trade deal can be fair for both sides.
Trump told May "Let's do this deal."
The meeting with business leaders at St. James's Palace brings together nearly a dozen 10 leading companies from the UK and the United States.
Just up the street, protesters leaders of Britain's political opposition will be joining demonstrators. They are inflating a blimp depicting Trump as a giant screaming baby to protest his visit.
As Prime Minister Theresa May meets President Donald Trump in Downing St., leaders of Britain's political opposition will be joining protesters just up the street.
Labour Party leader Jeremy Corbyn and senior lawmakers from his left-of-center party will be among thousands of demonstrators expressing noisy opposition to Trump's visit on the streets of London.
Emily Thornberry, Labour's foreign affairs spokeswoman, says Trump is "a sexual predator" and a racist and does not deserve the honor of a state visit.
Trump has dined with Queen Elizabeth II at Buckingham Palace and taken tea with Prince Charles on his pomp-filled trip to the U.K.
Things are likely to become more awkward on Tuesday when he meets May, who is in the final weeks of her premiership. The two leaders have sharply differing views on issues including Iran, Brexit and Chinese telecoms firm Huawei.
Trump has already criticized May's handling of Brexit and said May's rival Boris Johnson would make an "excellent" prime minister.
President Donald Trump will turn from pageantry to policy Tuesday as he joins British Prime Minister Theresa May for a day of talks likely to highlight fresh uncertainty in the allies' storied relationship.
Britain is scheduled to leave the EU on Oct. 31 unless both sides agree to an extension. Its position is in flux because May is stepping down as party leader Friday, setting in motion a race to succeed her as prime minister.