Ninth seed Raducanu had led by an early break in the second set before Giorgi reeled off six games in a row to win in Toronto.

"I think it was a really good match, to be honest," said the 19-year-old.

"I just need to get better at dealing with players who play as quick as she does."

The US Open, where Raducanu memorably triumphed last year, begins on 29 August in New York.

The Toronto event is one of several hard court events before the final major of the season.

Raducanu reached the quarter-finals of the Citi Open last week, but could not find a way past 29th-ranked Giorgi.

The two traded early breaks in the opening set before Raducanu saved a set point to force an eventual tie-break.

Giorgi, 30, won all seven points in the tie-break to take it, but Raducanu hit back, winning the first two games of the second set.

However, the Briton could not hold on to her lead and did not hold serve for the rest of the set as Giorgi powered to victory.

Earlier, 10th seed Coco Gauff beat American compatriot Madison Brengle 6-1 6-3, and will face Wimbledon champion Elena Rybakina next.

Canadian Bianca Andreescu delighted the home crowd with a 7-6 6-4 victory over world number nine Daria Kasatkina.

After the match, the 22-year-old, who won the US Open in 2019, apologised after twice calling out the trainer, including during the first-set tie-break.

"I was honestly a mess," said Andreescu. "I'm so sorry for my attitude. I really do not feel well. I don't know what it was - maybe I ate too much before the match."

However, two-time US Open champion Naomi Osaka was forced to retire midway through her match against Kaia Kanepi. Osaka trailed 7-6 (7-4) 3-0 when she quit with a lower back injury,

"I felt my back from the start of the match, and despite trying my best to push through it, I just wasn't able to today," said Osaka.