"It is not something that I'm proud of, of course," Visnjic told the women's magazine Story. "But I am ready to accept all the consequences of my act."
Visnjic, who lives in Los Angeles and has also played alongside Nicole Kidman and George Clooney in Hollywood hits, has been married to Ivana Vrdoljak since 1999. The couple adopted a son this spring.
Mirela Rupic, a 36-year-old woman from Visnjic's hometown of Sibenik, sued Visnjic earlier this week, claiming that her 4-month-old daughter is his. Rupic wants him to take a paternity test and pay child support.
Visnjic said he "remembers nothing" from the night spent with Rupic while alone on vacation last summer, because he was jet lagged and had consumed alcohol.
"I was always against cheating," he said. "I still can't believe I did it."
Visnjic said he is ready for a paternity test and if it shows the child is his, he will pay child support but will not seek custody.
Visnjic, 34, has co-starred in the feature films "Elektra" with Jennifer Garner and "Practical Magic" with Kidman and Sandra Bullock. He also played in "Peacemaker" with Clooney.
The magazine did not say how and when it interviewed Visnjic. He could not immediately be reached for comment.