Usmagazine.com reported this week that a model gave an interview to the gossip Web site x17online.com, claiming she was a guest at the couple's wedding in July, started exchanging sexually explicit text messages with Parker Sept. 29 and had an affair with him shortly after.
Longoria's representative Liza Anderson dismissed the reports as "completely, 100 percent false and untrue."
"I love my wife," Parker said in a statement later issued to People. "She's the best thing in my life, and I have never been happier."
Longoria, who married Parker in July, added, "Tony has been nothing short of the perfect husband."