The world number 65 Ukrainian has been among the most vocal critics of the decision to allow Russian and Belarusian players to continue playing on the Women's Tennis Association (WTA) and Association of Tennis Professionals (ATP) Tours, albeit under a neutral flag, since the invasion.

Belarus neighbours Ukraine and is one of Russia's key allies in the conflict, and the International Olympic Committee has recommended that athletes and officials from both countries are banned from international sporting events.

Former world number one Azarenka, a two-time Olympic medallist, two-time Grand Slam winner and three-time runner-up at the US Open, beat Kostyuk 6-2, 6-3 in straight sets at Flushing Meadows.

After their encounter, Kostyuk held up her racket at the net to which Azarenka responded with a tap of hers, but did not offer the traditional handshake.

Kostyuk commented afterwards that she did not believe a handshake would be "the right thing to do in the circumstances I'm in right now".

"It's pretty personal," she said, as reported by the CBC.

"It wasn't a personal match for me because it was Vika specifically, but overall it was not just a casual match that I play in a tournament."

The 20-year-old Ukrainian texted Azarenka on the day prior to the match to inform her of her intentions.

Azarenka admitted that she "wasn't surprised" at not being offered a handshake, but said "I don't believe that making a big deal out of it is important".

"I cannot force anybody to shake my hand," the 33-year-old said.

"It's their decision.

"How did it make me feel?

"It's not the most important thing in the world right now."

Azarenka is a member of the WTA Player Council, and Kostyuk expressed her frustration that she had not used her position to show vocal support for Ukraine.

The Belarusian defended her work on the Player Council, arguing that "with all due respect, I don't think she has any idea of what I do on the Player Council", and insisting that "I am always available to players because it's part of my job".

"I know she's [Kostyuk] going through a lot of difficult situations," Azarenka said.

"It's not easy to handle.

"From my perspective, I wish she had somebody who guide her a little bit better through this difficult time.

"There is going to be more sympathy from others.

"I feel like when you're trying to react, it's not always received that well.

"So I'm always open to listen.

"I can't force people to do something they don't want to do, but any time, she has my number, as you know she texted me, and all others, as well.

"Whatever I can do to help people.

"I don't play political games, I don't play media games, that's not what I'm here for."

Azarenka had been due to take part in a Tennis Plays for Peace Exhibition event organised by the United States Tennis Association prior to the tournament to raise money for Ukraine, but was dropped from the line-up after criticism from players including Kostyuk over her participation.

Azarenka is known to have previously had a friendly relationship with Belarus' authoritarian President Alexander Lukashenko, but was criticised by the country's Minister of Sports and Tourism Sergey Kovalchuk last year for her failure to participate in the Tokyo 2020 Olympics.

Russia launched a full-scale invasion of Ukraine on February 24, assisted by Belarus, and Azarenka wrote on Twitter on March 2 that she was "devastated by the actions that have taken place over the last several days against and in Ukraine", and "it's heart-breaking to see how many innocent people have been affected".

She also called for "peace and an end to the war".

The match at the US Open was the first meeting between Kostyuk and Azarenka.

The US Open is tennis' final Grand Slam of the year.

The last Grand Slam was Wimbledon in June and July, which had its ranking points stripped by the ATP, WTA and International Tennis Federation due to organisers' decision to block the participation of Russian and Belarusian players.