Mrs May confirmed she will meet the US president in Washington DC on Friday after a weekend in which hundreds of thousands of people in Yorkshire and around the world joined women’s marches to protest against Mr Trump.
The PM said she will tell Mr Trump when she finds his behaviour or statements “unacceptable” - a criticism she has already levelled at him over his past comments about women.
Mrs May has previously used the term “unacceptable” to describe Mr Trump’s suggestion that his fame allowed him to “do anything” to women, such as “grabbing them by the pussy”.
The President’s repeated highly controversial remarks about women inspired massive “pink pussy hat” marches attended by at least 500,000 in Washington DC and 100,000 in London on Saturday.
The PM said the “special relationship” between the UK and US will allow her to criticise Mr Trump where she sees fit.
Asked if she would raise the controversial tycoon’s treatment of women at their meeting, Mrs May told BBC One’s Andrew Marr Show: “I have already said that some of the comments that Donald Trump has made in relation to women are 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 United Kingdom, directly taking to him about the interests that we share.”
The PM highlighted her “track record” in defending the interests of women, including moves to tackle modern slavery and domestic violence while home secretary.
She said she was “proud” to be the second female premier, adding: “I will be talking to Donald Trump about the issues that we share - about how we can build on the special relationship, it’s the special relationship that also enables us to say when we do find things unacceptable.”
Mrs May added: “Whenever there is something that I find unacceptable I will say that to Donald Trump.”
Mrs May insisted Mr Trump was looking for “early” talks on a UK-US free trade deal despite his “America first” strategy sparking concerns that he would not be willing to reach an agreement.
“He and people around him have also spoken of the importance of a trade arrangement with the United Kingdom and that is something they are looking to talk to us about at an early stage, and I would expect to be able to talk to him about that alongside the other issues I will be discussing with him when I am in Washington,” she said.
Mrs May has also spoken of reducing barriers to trade before a formal deal can be reached after Brexit, amid reports of potential moves to set up a “passporting” system for transatlantic banking.
And she defended Mr Trump’s widely criticised “America first” message: “If you think about it, any leader, any government, as we do here in the United Kingdom when we look at any issue, we ensure that we’re putting the UK’s interests and the interests of British people first.”
The Prime Minister insisted Mr Trump was committed to Nato despite worries that he has consistently undermined the mutual defence alliance at a time of Russian aggression.
At their meeting, the pair could agree a statement emphasising their commitment to spending at least 2% of GDP on defence and urging other Nato countries to match them, according to reports.
Mrs May said: “I’ve spoken to him about Nato - Nato is very important, Nato has been the bulwark of our security here in Europe and we work together in Nato,” she said.
“We’ve both made the point before about contributions being made by countries, the United Kingdom is spending 2% of its GDP on defence, I believe that’s important.”
She added: “What is important is that we recognise the value of Nato, which he does, the value of Nato as an organisation that is helping us to defend Europe and defend the interests of all of those allies who are in Nato.”
Mrs May also suggested her visit would be followed by a state visit by Mr Trump to Britain this year, which would include an audience with the Queen and the pomp and pageantry of which the President seems so fond.
“I would look forward to welcoming President Trump here to the United Kingdom sometime this year if that’s possible but of course in terms of state visits that’s a matter for Buckingham Palace and they haven’t announced the visits this year yet,” she said.
Jeremy Corbyn urged Mrs May to directly criticise Mr Trump’s misogyny and his call for Muslims to be banned from the US.
The Labour leader told Sky News’ Sophy Ridge on Sunday: “There were no signs of any special relationship in Donald Trump’s inauguration speech, it was quite the opposite.
“It was America first, America only, America inward-looking.
“I would hope that when she meets Donald Trump she will in no uncertain terms tell him that his misogyny during the election campaign, the way in which he described Muslim people and others of different faiths, the way in which he proposes to build a wall between his country and Mexico, is simply not acceptable and not the right way of going forward.”
Mr Corbyn warned Mrs May to be “extremely careful” in negotiating a free trade deal with Mr Trump, warning that it could be unfavourable to the UK.
“The idea that Donald Trump is suddenly going to roll over and offer some trade deal with Britain that doesn’t have strings attached, like investor protection where American companies can come in and run parts of our health service and be protected in doing so - I think she needs to be extremely careful,” he said.