The woman shared screen shots with Babe of a text conversation she says took place the day after the incident, in which she wrote, "I just want to take this moment to make you aware of this behavior and how uneasy it made me."
» Aziz Ansari shares emotional story about dad and 'Master of None'
On Sunday, the actor issued a statement, sent to USA TODAY via his representative Jodi Gottlieb, saying he reached out to the woman "after taking time to process" her accusations.
"In September of last year, I met a woman at a party. We exchanged numbers. We texted back and forth and eventually went on a date. We went out to dinner, and afterwards we ended up engaging in sexual activity, which by all indications was completely consensual.
"The next day, I got a text from her saying that although "it may have seemed okay,' upon further reflection, she felt uncomfortable. It was true that everything did seem okay to me, so when I heard that it was not the case for her, I was surprised and concerned. I took her words to heart and responded privately after taking the time to process what she had said.
"I continue to support the movement that is happening in our culture. It is necessary and long overdue."
Ansari, a two-time Emmy winner for his Netflix show, won best actor in a TV musical or comedy series last Sunday at the Golden Globes. He wore a Time's Up pin on the red carpet showing his support for the initiative devoted to addressing men's abuse of power and gender inequity.