"I have no comments to you, so thank you for your question," she told a news conference before a reporter asked about her relationship with Belarus president Alexander Lukashenko and whether a potential world number one should be associated with him. Sabalenka has met Lukashenko in the past.
Lukashenko, Russian President Vladimir Putin's staunchest ally among its neighbours, celebrated Sabalenka's Australian Open victory in January and said recently that people knew which country she hailed from even if she was playing under a neutral flag.
"I've got no comments to you," she said. "You've got enough answers from me, and I've got no comments to you."
Sabalenka said on Sunday that no Russian or Belarusian athlete supported the war.
In March 2022, tennis's governing bodies barred players from Russia and Belarus from competing under the name or flag of either country due to the war, requiring them to play under neutral flags.
Sabalenka will take over the number one spot from Iga Swiatek of Poland if she wins the Grand Slam tournament in Paris.
Kostyuk had refused to shake Sabalenka's hand after losing to her 6-3 6-2 on Sunday and urged her to take a stronger, more personal stand against the war.
"She (Sabalenka) never says that she personally doesn't support this war, and I feel like journalists should change the questions you ask these athletes because the war is already there," Kostyuk said.