Kyrgios described Tomic as the most hated athlete in Australia when the pair exchanged barbs over who was the better player on Instagram on Wednesday night.
Tomic, who won their only professional meeting at Kooyong in 2019, returned serve by offering to put up a million dollars for a one-on-one contest.
“At the end of the day, talk is cheap,” Tomic told the Sydney Morning Herald. “I’m ready to make it 2-0 whenever you want. Put your money where your mouth is.
“Let the public decide who is better. I’ll beat you anywhere, any place. If not, shut your mouth and go back to playing doubles.
“I’ll dominate you one-on-one,” he added. “To not make excuses, I’ll even play you on grass, whenever you want.
“You know what? Let’s sort this out in the boxing ring. Put your gloves on, I’ll dominate you there also. Let’s see who’s better once and for all.”
Kyrgios did not rule out a boxing bout one day but said the world number 418 would have to work his way back up the rankings to get on court with him.
“I’m still playing on the tour, my brother. I’ve got bigger fish to fry,” the world number 76 said in an Instagram video.
“If you want to play me and you want to set this straight, just get back to the top of the sport. I’m right here, I’m not going anywhere.”
Kyrgios won his first Grand Slam doubles title at the Australian Open this year and also reached the singles quarterfinals at the $8.5 million Indian Wells tournament.
One-time prodigy Tomic, who reached the Wimbledon quarterfinals as a teenager, most recently lost in the first round of a $53,120 event in Mexico on the second tier Challenger tour.