May will be the first world leader to hold bilateral talks with the new US President when she meets him in Washington DC on Friday, White House has said.
The two leaders will hold talks on issues such as trade, and security but the British PM today also stressed that she would not shy away from addressing difficult issues.
"I will be talking to Donald Trump about the issues we share and how we can build on the special relationship. It is the special relationship that allows us to say when something is unacceptable. Whenever there is something I find unacceptable, I won't be afraid to say that to Donald Trump," she told the BBC.
Asked whether she would raise some of the comments that Trump had made about women during the presidential campaign, she said: "I have already said that some of the comments Trump has made in relation to women were unacceptable. Some of those he himself has apologised for.
"When I sit down, I think the biggest statement that will be made about the role of women is the fact that I will be there as a female prime minister, Prime Minister of the UK, directly taking to him about the interests that we share."
Asked about her views on some of Trump's protectionist rhetoric on trade in his inauguration speech earlier this week, May highlighted that he had also spoken about the importance of a "trade agreement with the UK" and that is something the US wants to begin working on at an early stage.
She said the Trump team is interested in discussing a new trade arrangement with Britain despite the "America first" theme of Trump's inaugural address and his vow to evaluate every trade deal for its possible benefits to the United States.
She said the US and UK had a deep and broad-based relationship, spanning a range of shared interests and values.
She noted: "There are issue that we will work on together in the future - the importance of NATO and defeating terrorism.
"These are issues where we share the challenges and see the threats, where we have worked together in the past and will do so in the future."
The British PM is set to fly out to Washington DC later in the week for what is expected to be a two-day visit to the US.
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