Theresa May will this week travel to meet Donald Trump for talks about Nato, post-Brexit trade and fighting terrorism, but indicated she would not raise his comments about women despite branding them as unacceptable.

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The prime minister was repeatedly pressed about whether she would challenge the US president on Friday about sexism after up to 2 million people joined women’s marches around the world on Saturday to protest against him. More than 80,000 people gathered in London.

However, she told BBC1’s Andrew Marr Show that being a female prime minister and the first foreign leader to meet Trump since his inauguration would be the “biggest statement” she could make about the role of women in the world.

May said she had previously expressed concerns about some of his comments – such as the video of Trump talking about grabbing women “by the pussy” – and insisted she was unafraid to raise concerns with Trump when necessary in future. However, the talks will concentrate on “pressing global issues” including terrorism, Syria, relations with Russia and cooperation in Nato.

“I’ve already said some of the comments Donald Trump has made in relation to women are unacceptable. Some of those he has apologised for. When I sit down, I think the biggest statement that will be made about the role of women is that I will be there as a female prime minister, directly talking to him about the interests we share.

“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 … Whenever there is something that I find unacceptable, I will say that to Donald Trump.”

Trump is expected to host May for discussions in the White House’s Oval Office on Friday before she heads to Philadelphia to become the first foreign leader to address the annual retreat of Republican politicians.

The British embassy in Washington confirmed that the prime minister had been invited to address Congressional members of Trump’s political party “as a result of the efforts the UK government has made to establish strong links with the new administration”.

Discussions over Nato are expected to be at the heart of the White House talks, after Trump suggested he wanted major changes to its funding and that the organisation was obsolete.

Ted Malloch, tipped to be the next US ambassador to the EU, told the BBC’s Sunday Politics that Nato may be “reformed and reshaped” under Trump’s administration, with the potential for “more burden sharing” among members.

But May insisted on Sunday that her conversation with the president indicated he was committed to Nato. “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.”

In a first potential alliance, the pair could agree a statement at the end of the week emphasising their commitment to spending at least 2% of GDP on defence and urging other Nato countries to match them.

No 10 said May would be carrying a message to Washington about the continuing importance of Nato after revealing that the prime minister spoke to Jens Stoltenberg, the alliance’s general secretary, on Sunday afternoon.

A No 10 spokesperson said: “They discussed the continued importance of the alliance as the bulwark of our defence and agreed on the need for the alliance to continue to evolve to be able to effectively counter the biggest threats of the day, in particular terrorism and cyber attacks.”

May and Trump will talk about the possibility of a UK-US trade deal after Brexit, after the president said he wanted to get one signed as soon as possible. May is enthusiastic about the prospects of a deal, despite warnings from Labour and others about the dangers of different environmental and food safety standards as well as the potential for US companies to run parts of the NHS.

Downing Street has been attempting to build diplomatic relations with Trump after a rocky start when he expressed a desire to see the former Ukip leader Nigel Farage become the British ambassador to Washington.

As part of the attempt to woo the US president, the Queen is likely to extend an invitation to Trump for a state visit this summer. May said she would “look forward to welcoming president Trump some time this year if that is possible”.

The prime minister has been careful not to be too critical of Trump, although a number of other senior Conservatives have shown no such restraint. George Freeman, the head of the prime minister’s policy board, tweeted that the inauguration speech was “unusually and deliberately divisive and confrontational”.

Asked about Trump’s inaugural speech, May said the US president had a very clear message of putting America first, just like all governments worked for the interests of their own people. “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,” she said.

Jeremy Corbyn, the Labour leader, warned May that she needed to be careful about striking a trade deal with Trump and urged her to challenge his misogyny and comments about Muslims.

He told Sky’s Sophy Ridge: “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 when she meets Donald Trump she will, in no uncertain terms, tell him 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.

“The idea that Donald Trump will suddenly roll over and offer a trade deal with Britain, which doesn’t have strings attached like investor protection, where American companies can come in and run parts of our NHS and be protected in doing so … I think she needs to be extremely careful.”