Leaders say a message posted on Twitter, which read: "Prayers for Prof Dawkins and his family" was "nothing controversial" but "a genuine tweet offering prayer for a public person who was unwell".
They also acknowledged tweet has created a "Twitterstorm", while some users criticised it as "provocative", "insensitive" and "disrepectful".
One Twitter user, @George_Richford, said: "It was provocative. If you genuinely wanted to offer prayers, a personal conversation with God, there was no reason to go public."
Meanwhile, others have rallied behind the Church of England, describing the offer of prayer for Prof Dawkins as "a great response" and "It looks like a summation of the Christian message in a tweet to me".
Twitter user, @gtomlin, said: "Can't believe [The Church of England] is having to defend it's tweet about Richard Dawkins. Don't people know we are supposed to love our enemies?"
The Rev Arun Arora, Director of Communications for the Archbishops' Council, said: "The prayer tweeted on Friday evening was for Richard Dawkins. It's hardly surprising that I don't agree with all of his views (viz his most recent tweet on Dan Walker).
"Any suggestion that Christians do anything other than hate Professor Dawkins utterly confuses those who think in binary terms.
"Few would appreciate that the former Archbishop of Canterbury, Rowan Williams, hosted Richard Dawkins and his wife at a party at Lambeth Palace in 2007.
"I wish Professor Dawkins well. I hope he makes swift and full recovery and wish him the best of health. I will pray for him too. It is the very least I can do."
Prof Richard Dawkins, who has been outspoken in his promotion of a secular worldview, has been recovering from a stroke he suffered on Friday 5th February.
The stroke left him at The John Radcliffe Hospital in Oxford for four days.
In a message posted online, Prof Dawkins said: "I'm very grateful to everybody whose been sending me good wishes from all around the world. I'm at home and I appear to be improving. Many thanks."