The Supreme Court said it would refer the request to the Serbian Assembly, which decides on such matters. If the Assembly fails to decide on the request within a month, the judge will be relieved of his duties automatically.
Some analysts in Belgrade believe that Kljajevic has been under pressure, particularly since his brother, who until recently was president of the Belgrade Commercial Court, was arrested on corruption charges.
Several political parties on Friday expressed fear that Kljajevic's move might badly affect the already protracted trial, which was expected to be completed by the year's end.
Djindjic was shot dead by a sniper outside government headquarters in Belgrade in March 2003. The first accused is Milorad Ulemek Legija, former commander of the now dissolved special operations unit known as the Red Berets. Another 11 men, some of whom were members of the same unit or of the criminal gang called the Zemun Clan, are also charged. Five of them are still on the run.