On Saturday, the model, 51, was photographed kissing Fuqua, 53, by a hotel’s pool in Italy. Fuqua has been married to actress Lela Rochon since 1999 and the pair shares two children: daughter Asia, 16, and son Brando, 15. The director also has a son, Zachary, from a previous relationship.
“Antoine and I friends. We ran into each other while we both were in Europe,” Murphy said in a statement obtained by PEOPLE. “Without going into the entire situation, I want to apologize to my family, and to Lela and the Fuqua family for what transpired.”
She continued, “It was not my intention to be in this situation. I do not condone women kissing or interacting in anyway [sic] inappropriately with a married man.”
“I too was once married and I would never intentionally undermine another woman, despite what has been written,” she added.
Shortly after being spotted getting close with the filmmaker, Murphy also told LoveBScott.com that the two “are just family friends.”
“I ran into him in Italy and we exchanged a friendly hello and that was it,” she told the outlet.
Murphy and Fuqua shared a kiss while in Italy on Saturday. The two were in town for the Ischia Global Festival where Fuqua, who directed Training Day, received the director of the year award.
Both held coffee cups as they shared a kiss, with Fuqua wearing a navy towel around his waist, while Murphy wore a bikini and a white sheer robe.
A source told PEOPLE earlier this week, Fuqua and his actress wife “were both together a few weeks ago at their son’s basketball game and looked like a happily married couple.”
“She was wearing her ring and they seemed perfectly happy,” the insider added.
A second source told PEOPLE of Fuqua and Murphy, “It’s known that they’ve been close friends for a long time and travel in the same circles.”
After the news broke, Rochon deleted both of her Twitter and Instagram accounts.
Murphy was previously married to Eddie Murphy from 1993 to 2006 and the former couple has five children together: son Miles, 26, and daughters Bria, 19; Shayne, 24; Zola, 19; and Bella, 17.
She dated Good Morning America‘s Michael Strahan from 2009 to 2014.