"I am not trying to take any more attention away from the matches in Cincy, but I have been reading reports that I did not apologise for my comments, which is untrue," Kyrgios said in a statement posted on Facebook.
"I privately and publicly apologised immediately after the match last week.
"There is no blame game, I take full responsibility for what was said and for what has been a difficult learning experience," he said.
In remarks made to a Canadian newspaper earlier this week, Vekic, 19, said she had not received any communication from Kyrgios over the incident.
"I haven't spoken to Kyrgios. But it's a very disappointing thing to be happening in our sport and I hope it won't happen again because it's not a very good image for our sport," she said.
-AAP