Mr Trump and his wife Melania ignored questions from reporters as they touched down in Belgium late on Tuesday.
He set the tone for his attendance at the two-day alliance summit starting on Wednesday in Brussels with a combative tweet reminding the Europeans that the US spent “many times more” on their defence than any other alliance member.
“Not fair to the US taxpayer,” he wrote, “Nato countries must pay MORE, the United States must pay LESS. Very Unfair!”
The president’s intervention is likely to increase nervousness among European and Canadian leaders about Mr Trump’s commitment to the alliance and the wider international following the acrimonious break-up of the G7 summit in Quebec in June.
Ahead of the gathering, Mrs May was keen to emphasise that as well as supplying additional troops for Afghanistan, the UK was one of just five alliance members to meet the target of spending 2 per cent of GDP on defence.
“The alliance can rely on the UK to lead by example, not just in meeting the 2 per cent pledge but by contributing our cutting edge capabilities to operations around the world,” she said.
“In committing additional troops to the Train Advise Assist operation in Afghanistan we have underlined once again that when Nato calls the UK is among the first to answer.”
The extra troops, from the Welsh Guards, will bolster the UK-led Kabul Security Force which provides protection for Nato civilian staff engaged in capacity-building programmes in Afghanistan, as well as mentoring Afghan forces in the capital.
They will begin deploying in August with a second contingent to follow in February taking the total UK military presence in the country to 1,100.
In a momentous week for Anglo-US relations, Mr Trump will follow his attendance at the Nato summit with his first visit as president to Britain before going on to hold talks with Vladimir Putin in the Finnish capital Helsinki.
He is due to be met with mass protests across the UK including plans for a giant balloon of the president as a baby to be flown over Westminster.
The trip comes amid political chaos within Mrs May’s cabinet over her Chequers Brexit plan.
Brexit Secretary David Davis and Foreign Secretary Boris Johnson both sensationally quit earlier this week.
Mr Trump threw plans for an acrimonious trip into further disarray as he suggested Britain was in “turmoil” and that it was “up to the people” whether they wanted to keep Mrs May as Prime Minister just before leaving Washington.
He also suggested he could find time to talk to his “friend” Mr Johnson and that he would find it easier dealing with Mr Putin than America’s European allies.
The meeting with Mr Putin also comes days after Dawn Sturgess, 44, died after being poisoned by Russian nerve agent Novichok believed to be left over from an attack on ex-spy Sergei Skripal and his daughter Yulia.
The president also ruffled feathers with decidedly undiplomatic remarks before leaving Washington, saying Britain was in “turmoil” and that it was “up to the people” whether they wanted to keep Mrs May as Prime Minister.
“So I have Nato, I have the UK, which is in somewhat turmoil. And I have Putin. Frankly, Putin may be the easiest of all”, as he and his wife Melania prepared to board the Marine One presidential helicopter on the White House lawn.
Mrs May, for her part, insisted that she was looking forward to meeting the president, both in Brussels and when she hosts him in the UK.
“There’s much for us to discuss.
“As you know, the special relationship we have to the United States is our longest and deepest defence and security relationship, so we will be talking about those issues but also talking about trade issues,” she told a press conference to mark the end of the Western Balkans summit in London.
“There are particular issues between the EU and the United States because of the trade tariff issue at the moment, when he imposed those tariffs on steel and aluminium and the EU responded.
“We will be talking positively about how we can continue to work together in our special relationship for the good of people living in the UK and the United States and, actually, for the wider good.”