Spectators at the DC Open were warned that Ukraine's Elina Svitolina would not shake hands with Victoria Azarenka.
During the Russia-Ukraine conflict, Svitolina has refused to shake hands with opponents from Russia or Belarus.
Belarusian Azarenka was booed after Svitolina beat her at Wimbledon and to avoid a repeat, the scoreboard showed a message during Svitolina's 7-6 (7-2) 6-4 first-round win in Washington DC.
"It's the right thing," said world number 27 Svitolina.
"I asked for the WTA [Women's Tennis Association] to respect the decision of Ukrainians and they did."
At the end of the match, both players headed straight to the sidelines and the umpire.
Two-time Australian Open champion Azarenka, playing on her 34th birthday, said the warning to fans had arrived "18 months too late" and asked whether it was a big story.
"We just move on. We play a tennis match. As I said in Wimbledon, I accept, respect somebody's position. That's it," she added.
Both players had failed to clinch the first set on their own serve before Wimbledon semi-finalist Svitolina won it in a tie-break.
The message was shown after the first set, and there was just one hold of serve in the second as 28-year-old Svitolina sealed victory over the world number 19.
Wimbledon 2023: Elina Svitolina vows no handshakes with Russian and Belarusian players
