Speaking out of court on Monday, four legal team members said judge Marko Kljajevic should go because he was in the pocket of another mafia gang operating in the Belgrade area.
In a separate issue, special prosecutor Jovan Prijic asked that proceedings be separated from those of a dozen other suspects charged with unrelated crimes.
The so-called Trial of the Century, as it has been dubbed by the Serbian media, began on 22 December, but has been bogged down by legal technicalities and no evidence has been heard so far.
Djindjic was shot by a sniper outside a government building in central Belgrade on 12 March 2003.
His death shook the Balkan country and hastened the disintegration of the moderate alliance which had ruled Serbia since former Yugoslav president Slobodan Milosevic was toppled from power in 2000.
Alleged mafia boss Milorad Lukovic, an ex-chief of the Red Berets secret police unit who is better known as Legija, is accused of masterminding the assassination along with another crime boss, Dusan Spasojevic.
Courtroom One's Trial of the
Century has not met expectations
Legija and six of his alleged accomplices are still at large, while Spasojevic was killed in a confrontation with police in Belgrade on 27 March.
The alleged trigger man, Zvezdan Jovanovic, a former Red Berets deputy commander has been arrested, but claims he is being framed by the government. He has refused to enter a plea.
According to the indictment, the gang was planning a sustained campaign of violence and assassinations to overthrow the government.
They had "created a conspiracy with the goal of executing criminal acts against the constitutional order and the security" of the country "with the goal of achieving profit and power" it said.
Djindjic had stirred up a hornet's nest of enemies with his decision to extradite former nationalist strongman Milosevic to the UN war crimes tribunal at The Hague in 2001 and his efforts to crack down on organised crime.