Timberlake took to Instagram on Wednesday to say he prefers to “stay away from gossip.”
“I stay away from gossip as much as I can, but for my family I feel it is important to address recent rumours that are hurting the people I love,” the 38-year-old singer wrote.
“A few weeks ago I displayed a strong lapse in judgement — but let me be clear — nothing happened between me and my costar.
“I drank way too much that night and I regret my behaviour. I should have known better.”
He said that this is not the example he wants to set for his son.
“I apologize to my amazing wife and family for putting them through such an embarrassing situation, and I am focused on being the best husband and father I can be. This was not that,” the former NSYNC singer wrote.
“I am incredibly proud to be working on Palmer. Looking forward to continuing to make this movie and excited for people to see it.”
Timberlake is filming the movie Palmer with Wainwright in New Orleans. He married Biel in 2012 and they have a son, four-year-old Silas.
In November, Timberlake was photographed drinking with Wainwright. Several pictures and videos were shared of the pair online.
—With files from the Associated Press