“You have been condemned to the next life, your end is nigh,” said one anonymous letter sent to Cohen, the reports carried by both public and independent television channels said.
Police suspect that the threats are the work of hardline settlers angry at a 10-month moratorium on permits for new settler homes in the West Bank outside annexed Arab east Jerusalem, the reports added.
But they have not entirely ruled out a gangland connection.
Police are responsible for enforcing the new building restrictions in the settlements.
The police spokesman was not immediately available for comment.