Naomi Osaka cruised into round three in the night session at the US Open ©Getty Images

Fourth seed Naomi Osaka of Japan cruised into the third round of the US Open with a straight-sets victory over Italian Camila Giorgi in New York City.

Osaka, the 2018 US Open champion, recorded a 6-1, 6-2 win at Flushing Meadows to set-up a meeting with Ukraine's Marta Kostyuk.

Kostyuk, the world number 137, progressed after overcoming Latvian 31st seed Anastasija Sevastova – conqueror of American Coco Gauff in round one – 6-3, 7-6.

Osaka had been suffering from a hamstring injury in the lead-up to the tournament but showed no signs of distress in the commanding performance.

The Japanese star has brought seven different face masks – each bearing the name of an African-American who has died – as part of her efforts to continue to highlight racial injustice in the United States.

Fourth seed Stefanos Tsitsipas beat American Maxime Cressy to reach the third round of the men's draw ©Getty Images
Fourth seed Stefanos Tsitsipas beat American Maxime Cressy to reach the third round of the men's draw ©Getty Images

"Tennis – people watch it all around the world," Osaka said. 

"Things that we think are common names are not common overseas.

"I just want people to have more knowledge. 

"I feel like the platform I have right now is something I used to take for granted and I feel like I should be using it for something."

In the men's draw, fourth seed Stefanos Tsitsipas of Greece beat American Maxime Cressy 7-6, 6-3, 6-4.

Tsitsipas will take on Croatian Borna Ćorić in the third round after he defeated Argentina's Juan Ignacio Londero 7-5, 4-6, 6-7, 6-2, 6-3 in a marathon contest.