Bivol is preparing to defend his WBA regular light heavyweight title against Saul 'Canelo' Alvarez on May 9 as his opponent bids to become a two-time champion at 175lbs.
After Canelo confirmed his two-fight deal with Matchroom Boxing, he held a press conference to promote his fight with Bivol in San Diego on Wednesday.
However, the ongoing crisis in Ukraine soon became a talking point at the media event.
Bivol, undefeated from 19 professional bouts, has been a long-time resident of St Petersburg and is a Russian citizen but has not vocally supported Russia's President Vladimir Putin.
The 31-year-old, originally born in Tokmak, Kyrgyzstan, said: "I have a lot of friends in Ukraine,' Bivol said. 'I have a lot of friends in Russia. My family is in Russia.'
"It's really sad for me. Every day I wake up and read the news and I hope it will stop."
Bivol was asked about both Ukrainian fighters and told FightHype: "It is hard to comment on something related to people defending their home country.
"As athletes, I respect them a lot, they are some of the best in the world and as people, I respect them a lot.
"But their choices and the things that they do, it is very individual. I make my own choices, they make their own choices. They have to do what they do."
Bivol is still scheduled to face Canelo despite the WBC, IBF and WBO delivering a series of sanctions this week.
Russian and Belarusian boxers will be stopped from entering the ring with their flag nor will the respective national anthems be played.
However, a recent WBA statement suggests if the fight does happen then it will be without a title on the line.
"Russian and Belarusian officials will also be banned from participating in world and/or regional championship fights, according to a resolution from the WBA Executive Committee."