Victoria Azarenka was not concerned by being shunned by Marta Kostyuk at the US Open, adding that she has tried to contact the Ukrainian throughout the year.
Kostyuk elected not to shake hands with Azarenka following a second-round defeat at Flushing Meadows, instead merely tapping rackets.
That came after Kostyuk criticised the Belarusian for participating in a charity match for Ukraine, before the United States Tennis Association announced she would no longer be involved.
Belarus maintains close ties with Russia and has been under sanction from western nations for supporting Vladimir Putin after the Russian invasion of Ukraine in March.
Both situations led to a frosty atmosphere following the conclusion of the tie, which Azarenka won 6-2 6-3.
"Well, I wasn't surprised. I don't believe that making a big deal out of it is important. I always shake hands with my opponents. I had the same situation with [Dayana] Yastremska in Washington. It is what it is. I just move on. I cannot force anybody to shake my hand. It's their decision," Azarenka said in a press conference.
Asked if she had spoken to Kostyuk, Azarenka added: "I've offered many times through WTA, because I believe that there is a sort of sensitivity. I've been told that that's not a good time.
"I don't have, or I never had a close relationship with Marta. I obviously knew who she is, but I've never practiced with her. I've never really had conversation with her.
"So in March when everything happened, I reached out to all the players that I personally know and I still have a good relationship with and, you know, I don't feel that forcing myself to speak to somebody who maybe doesn't want to speak to me for different reasons is the right approach. But I offered."
Kostyuk was asked about the decision not to shake hands and explained her reasons, saying she believed it was not "the right thing" in the current climate.
"I just don't think it's the right thing to do in the circumstances I'm in right now," she said.
"We had a great match, don't get me wrong. She's a great competitor, I respect her as an athlete but that has nothing to do with her being a human being."