Jabeur, 29, had treatment from medical staff in the first set and had her blood pressure taken during a timeout.

"I have the flu, so it wasn't easy to play," said Jabeur, who also lost in the New York final last year.

"I also have a history of asthma. So it was a very, very tough day for me."

Second seed Aryna Sabalenka overcame a poor start on serve to win her opening match against Belgium's Maryna Zanevska.

The 25-year-old Belarusian hit five double faults as she was broken in her first two service games, including three in a row on her way to falling 2-1 down, but found her rhythm to recover.

"If I were you I would've left after the third double fault, so thank you for staying and being patient," the Australian Open champion, who plays Britain's Jodie Burrage next, told the Flushing Meadows crowd.

Two-time champion Venus Williams, given a wildcard at the aged of 43, lost 6-1 6-1 to Belgium's Greet Minnen on what was a record-extending 24th singles appearance in the Open era.

French seventh seed Caroline Garcia lost 6-4 6-1 to world number 114 Wang Yafan of China.

Garcia reached the semi-finals at Flushing Meadows last year but has not come close to replicating that result this year, falling at the first hurdle on court five.

Elsewhere on Tuesday, there were wins for third seed Jessica Pegula, Wimbledon champion Marketa Vondrousova, Ukraine's Elina Svitolina and American Madison Keys.

'I didn't have the best attitude' - Jabeur

Fifth seed Jabeur, last year's beaten finalist, is bidding to go one better in 2023 and land her first Grand Slam title in the process.

Her campaign got off to a shaky start, though, in a first-round match against world number 68 Osorio that featured 13 breaks of serve.

"I did consider retiring, to be honest, so many times," Jabeur added.

"But every point, I kept going. I wanted to push myself to my limits. I'm glad I was able to fight.

"It wasn't an easy match. I know at some point I didn't have the best attitude on the court."

She had taken a 4-1 lead in the first set but told the umpire she was struggling with her breathing after Osorio pulled it back to 4-4.

The two-time Wimbledon finalist had a medical timeout at 5-4 down before she roused herself to win the set 7-5.

Jabeur missed two match points when 5-3 up in the second set as 21-year-old Osorio forced a tie-break.

However, Jabeur proved too strong for the Colombian and will now face Czech Linda Noskova in the second round.

What else happened on day two?

American Pegula began her US Open bid with a 6-2 6-2 win over world number 52 Camila Giorgi on Arthur Ashe Stadium.

Picking up where she left off in SW19, Czech Vondrousova beat South Korea's Han Na-lae 6-3 6-0 to reach the second round.

Former US Open finalist Keys secured a straight-set victory over world number 45 Arantxa Rus, winning 6-2 6-4 on Louis Armstrong Stadium.

Wimbledon semi-finalist Svitolina beat Germany's Anna-Lena Friedsam 6-3 6-1 on court 17 as the Ukrainian 26th seed returned to Flushing Meadows having missed last year's event while pregnant with her daughter.

Meanwhile, Russian 13th seed Daria Kasatkina came from a set down to beat American Alycia Parks 2-6 6-4 6-2 to reach the second round in New York for just the second time in five years.

Czech Marie Bouzkova, seeded 31st, saw off a spirited challenge from American wildcard Ashlyn Krueger with a 7-5 6-4 win.

On court 11, 14th seed Liudmila Samsonova clinched a 7-6 (7-3) 6-3 win over Krueger's compatriot Claire Liu.