I would like to express Dear Father Rossi. But I do not want to use the word Caro.
Is this correct?
Egregio Padre Rossi,
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According to this page a formal salutation could be
Reverendo Padre Rossi
is slightly less formal.
Also according to the same page, the letter should end with a phrase like
La prego di accogliere, Reverendo Canonico (NAME AND SURNAME) l'espressione dei miei sentimenti deferenti
(YOUR NAME AND SURNAME)
Con rispetto e devozione in Cristo, (YOUR NAME AND SURNAME)
I would have suggested also Stimato but I guess it is not used and Egregio would be better.