The daily said that several letters with death threats arrived in the President's Office in the past two days.
According to one of the letters, Marovic's life is in jeopardy because he is advocating cooperation with the tribunal.
One of the letters criticised Marovic for daring to search for Ratko Mladic and said that criminal Milorad Lukovic Legija's men would be hired to kill him.
There have been no official reactions from the president's office yet. According to the daily, the cabinet of the European Union's High Representative for the Common Foreign and Security Policy, Javier Solana, has been informed about the letters.