In an interview with CBS News, the U.K. leader said Britain and America engage in "frank and open discussions," albeit they don't always see eye-to-eye.
"When we disagree… we can say to each other we disagree and why we disagree," May told the broadcaster. "But at the same time, we cooperate on so much else, which is of crucial importance to us."
May cited security and defense as two key areas on which the countries cooperate. Britain and the U.S. have shared what is known as an unwritten "special relationship" on matters including joint military operations and intelligence sharing for decades.
When asked whether she trusted President Trump, May said: "Well, yes. I mean, we work together. We have a special relationship. This is two people reflecting as leaders of their two countries – the relationship that those two countries have and have built up over a number of years."
She said the Trump administration's decision to expel 60 Russian diplomats in March in response to the poisoning of former Russian spy Sergei Skripal and his daughter in Salisbury demonstrated the close security relationship shared between the two countries.