The creator and star of comedy TV series Girls said she did not intend to "trivialise" terminating a pregnancy following comments she made during her Women Of The Hour podcast.
Dunham, 30, had recalled an incident at a Planned Parenthood meeting in Texas when she was asked to share a story about her own abortion.
She told listeners that she had never gone through the procedure, before adding: "But I wish I had."
Her comments prompted widespread accusations that she had trivialised abortion.
She was treating a termination "like getting your appendix removed", said one Christian organisation.
Right To Life of Central California said the remarks were "inflammatory and unhelpful".
John Gerardi, executive director, added: "Even if you accept the argument that women have a right to obtain access to abortions, we're still talking about another living human being.
"Even for pro-choice women, it's one of the worst and most difficult decisions of their lives.
"It seems Lena Dunham wants to treat abortions like getting your appendix removed."
In a post on Instagram alongside a picture featuring the word "Choice", Dunham said she was "proud" of the women who took part in the podcast which focused on the issue of abortion.
"I truly hope a distasteful joke on my part won't diminish the amazing work of all the women who participated," she wrote.
"I would never, ever intentionally trivialise the emotional and physical challenges of terminating a pregnancy. My only goal is to increase awareness and decrease stigma."
In the podcast, she claimed it was a "stigma" that she hadn't had an abortion.
She said: "So many people I love - my mother, my best friends - have had to have abortions for all kinds of reasons. I feel so proud of them for their bravery, for their self-knowledge, and it was a really important moment for me then that I had internalised some of what society was throwing at us and I had to put it in the garbage.
"Now I can say I still haven't had an abortion, but I wish I had."
