Babic committed suicide in the ICTY detention unit in the Hague district of Scheveningen on 5 March. He testified against Martic, his former partner in the rebel Serb government in Croatia in the 1990s.
ICTY President Fausto Pocar has ordered Judge Kevin Parker to conduct an inquiry into the circumstances surrounding Babic's suicide.
ICTY spokeswoman Alexandra Milenov told a news briefing on Wednesday that there were no news regarding the inquiry.
Babic's suicide has raised the legal issue of his testimony being used as evidence in the continuation of the Martic trial and in other proceedings before the tribunal.
Prosecutor Alex Whiting said on Wednesday that Babic's testimony should be accepted as valid, that it should stay in the case file, and that the trial chamber should be allowed to refer to it.
Defence Attorney Predrag Milovancevic said that Babic's hearing was not completed and that therefore his testimony was invalid and could not be used in the trial.
If it is true that he committed suicide, as was reported, the question arises as to his capacity to give evidence, Milovancevic said.
Both the prosecution and the defence announced they would present their views on the validity of Babic's testimony in writing.
After Presiding Judge Bakone Justice Moloto rejected the defence motion to adjourn the trial, Prosecutor Whiting called a protected witness identified as MM-003, who said that on 18 August 1990, the day when a state of war was declared in the main rebel Serb stronghold of Knin, he saw the accused Martic distributing weapons to Serb police reservists in the village of Golubic.
Martic is charged with war crimes against Croatian civilians committed in the Serb-occupied areas of Croatia from 1991 to 1995, war crimes committed in Bosnia-Herzegovina in 1994, and Serb missile attacks on Zagreb in May 1995.