The meeting was being watched with global interest as the two countries seek to find common ground on trade and lay the groundwork for a new deal following last year's Brexit vote in favour of the UK to leave the European Union. The two countries would also look to boost defence ties.
It would also be Trump's first tryst with face-to-face diplomacy as he welcomes his first foreign visitor to the Oval Office.
May said Britain and the US must "lead together" again and play their role in safeguarding global security even as she welcomed the rise of democratic allies like India.
"We have the opportunity to lead together again because the world is passing through a period of change. And in response to that change, we can either be passive bystanders or we can take the opportunity once more to lead and to lead together," she said.
"The rise of the Asian economies -- China, yes, but democratic allies like India too -- is hugely welcomed. Billions are being lifted out of poverty and new markets for our industries are opening up," she said.
May also paid her respects to the military dead of the US at Arlington National Cemetery outside Washington DC.
The UK Prime Minister laid a wreath at the Tomb of the Unknowns at the Virginia military cemetery, which holds the remains of unidentified US troops from the First and Second World Wars, as well as the Korean war.
A cannon was fired 19 times as the Prime Mminister's convoy arrived at the cemetery and made its way to the memorial, which stands on a small hill looking down over serried ranks of gravestones to the monuments of Washington a few miles away across the Potomac River.
The new US president and the premier, who took office in July, both have strong political incentives to make the visit -- likely to be heavier on symbolism and aspiration than deliverables -- a roaring success.
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