He said: “To be misunderstood by a man of such brilliant wit and insight means that I must have made a hash of my argument.”
In a letter to The Times the actor criticised the “sad reduction” of Jewish ritual.
Mr Berkoff wrote: “Laws are not meant to be ‘convenient’. They are there to protect and guide us out of the morass of self-importance and indifference to others.”
But Mr Finkelstein, who is also a JC columnist, said he had been making the same point as the actor.
“Rather than, as he seemed to fear, trivialising Jewish rituals, I was explaining why it might only seem trivial to those viewing it from outside.
“Various Jewish rituals must appear odd to non Jews and are not always easy for Jews to follow. Yet we follow them.
“They have meaning for us and we regard them as a liberation not an oppression or a difficulty.
He said the analogy he had made in his piece was that while those who are not devout Muslims may find the Burka odd, “for those who wear it, it is not an inconvenience or an oppression.”
Mr Finkelstein added: “I was surprised to read that I was in a war of words with the wonderful Mr Berkoff. But if I am, I surrender.”