The issue came up during Sunday's cabinet meeting after demonstrators during the past week shouted abuse at Finance Minister Binyamin Netanyahu and Education Minister Limor Livnat.
Transport Minister Meir Sheetrit received a letter reportedly saying: "You will see your children's funeral and we shall murder your wife and you."
The mood reminded Israelis of the atmosphere on the eve of Prime Minister Yitzhak Rabin's murder in 1995. A Jewish extremist killed him scuttling the peace process for a decade.
Infrastructure Minister Binyamin Ben-Eliezer showed Prime Minister Ariel Sharon a letter he had received and a person who read it told United Press International it was a clear, through not explicit, death threat.
Ben-Eliezer told the cabinet unless action is taken "we might attend more funerals.... The choice is between living in an orderly state or a state of Phalange."
Sharon gave the Justice Ministry two weeks to present a plan of action and asked the Shabak security service to report on the steps they are taking, a participant in the cabinet meeting reported.