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Prosecutor Ibro Bulic asked for Josipovic to be ordered into custody since he might influence witnesses, and for Tesic because he might to the same and flee to Serbia.
Bulic said he would finish the investigation within one month.
The Defence teams said the prosecution proposal was unclear and asked for the suspects to be released with prohibiting measures. The Defence proposed that the suspects be banned from meeting with witnesses and for Tesic to be banned from travelling.
The Court will make a decision at a later date.
The State Investigation and Protection Agency arrested on Thursday former Serb policemen Miodrag Josipovic and Branimir Tesic on suspicion that they assisted the commission of genocide in July 1995.
Police arrested Josipovic and Tesic on Thursday in the Bratunac region of north-eastern Bosnia on suspicion of ordering, organizing and overseeing the forced transfer of Bosniak civilians from Potocari near Srebrenica and the detention of several thousand imprisoned men and boys in Bratunac on July 13, 1995.
The prisoners were abused and around 100 were killed, according to the Bosnian prosecution.
Josipovic and Tesic are said to have been commanding officers at the Bratunac police station.
