PHOTO: AFP
In an interview with the Financial Times newspaper, May said: "I'm also confident the USA will recognise the importance of the cooperation we have in Europe to ensure our collective defence and collective security."
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The British premier is expected to visit Trump in the spring, according to Downing Street, although the FT reported that she could go to Washington as early as next month. Meanwhile May congratulated Trump after he took office on Friday.
"From our conversations to date, I know we are both committed to advancing the special relationship between our two countries and working together for the prosperity and security of people on both sides of the Atlantic," she said.
"I look forward to discussing these issues and more when we meet in Washington."
Earlier this week, before he was sworn in as president, Trump told two European newspapers he had long warned that NATO had "problems".
"Number one, it was obsolete, because it was designed many, many years ago," he said, referring to its Cold War, post-World War II origins. "Number two, the countries aren't paying what they're supposed to pay."
In his inaugural address on Friday, Trump said the United States had "subsidised the armies of other countries", highlighting a common cause of friction in the 28-nation alliance.
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In response to Trump's reported remarks about NATO earlier in the week, German Chancellor Angela Merkel warned Europe has to take responsibility for itself.
Meanwhile British Foreign Secretary Boris Johnson said billions of people were wishing Trump success in the "very great challenges" ahead of him.
"We in the United Kingdom will work hand in glove for the stability, the prosperity and the security of the world with President Donald Trump," he said in a statement.
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