The 63-year-old claims that Holbrooke made the promise during a meeting in Belgrade, Serbia's capital.
Karadzic was not at the meeting, but those present, including Slobodan Milosevic, the former Serb president, Jovica Stanisic, his intelligence chief, Momlico Krajisnik, the Bosnian Serb assembly speaker and Aleksa Buha, the foreign minister, told him of the detail, according to the motion.
Holbrooke has denied the existence of such an agreement, describing Karadzic's claim as "no more than another lie from the most evil man in Europe".
Karadzic has said Krajisnik and Buha could give evidence that Holbrooke offered the deal and claims he has 15 witnesses who support the claim. Stanisic is considered to be too ill to make a statement.
Milosevic died in 2006 while being tried for war crimes.
Peter Robinson, Karadzic's legal adviser, said documents included in the motion, such as statements, articles and a US government cable, should be enough for the tribunal to hold a hearing on the claims of an offer of immunity.
"Our hope is that they will at least have an evidentiary hearing. It's convincing enough for an evidentiary hearing for sure," he said.
The tribunal has said that any such deal would not be binding and could not grant Karadzic immunity from prosecution.
Holbrooke, the architect of the Dayton peace agreement that ended the Bosnian conflict, is now the US representative for Afghanistan and Pakistan.
Karadzic would face life in prison if convicted of charges over events related to the three-and-a-half year siege of Sarajevo, which left 10,000 people dead, and the massacre of 8,000 Muslims at Srebrenica in July 1995.
He was arrested on a Belgrade bus in July 2008, 13 years after he was first charged by the ICTY.
The tribunal entered not guilty pleas on Karadzic's behalf in March.