The newspaper said the letter was one of a number of death threats sent to Tadic since Kosovo declared unilateral independence from Serbia on February 17.
The Serb leader has been severely criticized by opposition parties for seemingly reconciling himself to the loss of Kosovo in exchange for guarantees from the EU after the signing of a Stabilization and Association Agreement (SAA).
The latest letter reads that Tadic "deserves a bullet in the head" for "betraying the Serbian people."
The presidential press service has yet to comment on the threats.
Serbian Prime Minister Zoran Djindjic was assassinated on March 12, 2003. Tadic subsequently replaced Djindjic as head of Serbia's Democratic Party.
Parliamentary elections are due in Serbia on Sunday. The main issue at the polls is whether Serbia moves closer to the EU or returns to hard-line nationalism.