The British author made the comment in response to another site user who said they would be faced with "a real ethical dilemma" if they became pregnant with a Down's Syndrome baby.
Professor Dawkins tweeted: "Abort it and try again. It would be immoral to bring it into the world if you have the choice."
He faced a backlash for his comment, with one mother, who has a child with the genetic condition, saying: "I would fight til my last breath for the life of my son. No dilemma."
Prof Dawkins later defended his view, saying he would not apologise "for approaching moral philosophic questions in a logical way".
Some users supported the God Delusion author, agreeing with his assertion that there is a difference in deciding on a termination before a child is born, and suggesting after the child is born that it should have been aborted.
The Down's Syndrome Association (DSA) issued a response to Prof Dawkin's initial comment.
They said: "People with Down's Syndrome can and do live full and rewarding lives, they also make a valuable contribution to our society.
"At the Down's Syndrome Association, we do not believe Down's Syndrome in itself should be a reason for termination, however, we realise that families must make their own choice.
"The DSA strives to ensure that all prospective parents are given accurate and up to date information about the condition and what life might be like today for someone with Down's syndrome.
Previously Prof Dawkins caused controversy on Twitter when he said the world's Muslims had won fewer Nobel Prizes than Trinity College Cambridge.