The actor, known for his comedy performances in Mr Bean and Blackadder, said the remarks were funny.
Atkinson wrote in a letter to The Times: "As a lifelong beneficiary of the freedom to make jokes about religion, I do think that Boris Johnson's joke about wearers of the burka resembling letterboxes is a pretty good one."
He added: "All jokes about religion cause offence, so it's pointless apologising for them.
"You should really only apologise for a bad joke. On that basis, no apology is required."
The Uxbridge MP said Muslim women wearing face coverings "look like letter boxes", and compared them to bank robbers and rebellious teenagers in a Telegraph column.
Mr Johnson is to face an investigation by an independent panel after complaints that his comments breached the Conservative Party's code of conduct.
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