The talks between Barasin, and Brammertz, who is on a working visit to the region before submitting his semi-annual report to the UN Security Council, were held behind closed doors in Sarajevo.
"The prosecutors have reiterated that their joint objective is to find and prosecute all cases of war crimes," reads a statement issued by the Office of the Bosnian Chief Prosecutor after the closed-door talks.
Brammertz also met with the international community's High Representative to Bosnia, Austrian diplomat Valentin Inzko, who "confirmed his continued support to ensuring that war criminals are brought to justice", according to a press release issued by the Office of the High Representative (OHR).
This support will be offered to ICTY "until the remaining fugitives are arrested and cases before the ICTY concluded," reads the OHR statement.
After meeting Bosnia's tripartite presidency, Brammertz expressed satisfaction with the cooperation with Bosnian agencies and authorities.
On Wednesday, the ICTY chief prosecutor will meet representatives of civil society associations gathering families whose loved ones were killed or went missing during the war.