Prof Dawkins described Peter Kearney, of the Catholic Media Office, as a "nasty little weasel" for calling for Mr Dallas, head of referee development at the Scottish Football Association, to be sacked. Mr Kearney's call came after Mr Dallas allegedly e-mailed a joke about the Pope.
Prof Dawkins, who said the Pope should be arrested on his visit to the UK in September claiming he had not done enough to investigate child abuse by priests, also used his website to describe Stewart Regan, chief executive of the SFA, as a "coward" and accused him of "craven giving-in to Catholic censorship".
In his opinion piece on the Richard Dawkins Foundation for Reason and Science website, Prof Dawkins includes a photo used in the e-mail incident and says: "My suggestion is that we should do our best to make this joke go viral, beginning by sending hundreds of copies of it to these two addresses"
He continues: "But there are probably funnier jokes along the same lines, and I would encourage you to send as many as you can find."
Last night Mr Kearney said: "Dawkins demonstrates again that his intolerance knows no bounds."
The SFA would not comment.