They were due to join the Canadian Prime Minister Justin Trudeau later at the Air Canada Centre to mark the start of the third Invictus Games – founded by the Prince in 2014 for wounded or traumatised war veterans.

The Prince and Trump shook hands warmly at the bilateral meeting at the Sheraton in Toronto which began at about 1.30pm local time.

Trump is in Toronto on her first solo foreign trip as First Lady to lead the US delegation to the Games.

Harry visited one of Canada’s top mental health facilities before the meeting and was greeted by huge crowds.

There is speculation the Prince will be joined at some point during his nine-day visit to Canada for the Games by his American actress girlfriend Meghan Markle, who lives and works in Toronto.

Harry, who also attended a Driving Challenge today, is due to be in Toronto until next Saturday (September 30).

About 550 competitors from 17 countries will compete in 12 sports.

US Master Sergeant Brian Williams, who had his left leg amputated at the knee because of an improvised explosive device in Afghanistan in 2012, said Harry is living up to the legacy of his late mother Diana with his charity work.

"He's following in his mother's footsteps," Williams told the Evening Standard.

"Straight up." 

He added he had a lot of respect for Harry, a former soldier who served in Afghanistan.

"He doesn't have to do this but he is," Williams said.

Williams competed at last year's Invictus Games in Orlando and is taking part in wheelchair basketball and sitting volleyball this year.

Canada’s Melanie Harris, who will compete in archery, suffered from severe post-traumatic stress disorder after serving two tours of duty as a medic in Afghanistan with the Canadian military.

"I was living without passion, without purpose. I needed to believe in myself again and I needed to be inspired," she said.

"And these Invictus Games, that's what they did."