The agency tweeted an apology to "anyone we offended", adding "we did not intend to capitalise on the passing of a great actor who contributed so much", although it does not appear to have taken down the post.
The piece is by New York-based executive vice-president Lisa Kovitz, titled ‘Carpe Diem’ and was published the day after the news of Williams’ suicide broke.
It opens: "As we mourn the loss of Robin Williams to depression, we must recognize it as an opportunity to engage in a national conversation.
"His death yesterday created a carpe diem moment for mental health professionals and those people who have suffered with depression and want to make a point about the condition and the system that treats it.
"There’s a very careful line they need to walk so as to not seem exploitive of a terrible situation but at the same time, it is a national teachable moment that shouldn’t be ignored. (We too are balancing that line with this post.)"
The apology came after a number of negative comments on the post and criticism from publications such as Gawker, which labelled it a "soulless PR conglomerate" in a sarcastic commentary on the piece.
"Having met a dead celebrity, or being afflicted with the same form of mental illness as a recently deceased celebrity, is quite a blessing in disguise for you, the Edelman client," Gawker wrote.