Ashdown and del Ponte met in The Hague on Wednesday to discuss progress made establishing the War Crimes Chamber in Bosnia-Herzegovina.
The lower house of the Bosnian Parliament is expected to debate on Thursday amendments to the Law on the Court and the Office of the Prosecutor and the law relating to the transfer of war crimes cases from the Hague tribunal to domestic courts.
"It is crucial that the Parliament adopt war crimes legislation so that Bosnia-Herzegovina can achieve its target and start with trials of war criminals by January," del Ponte said.
The High Representative and the Chief Prosecutor also said that there could be no compromise on the long-term commitment to the rule of law in Bosnia-Herzegovina.
"Independent and effective trials at the Bosnian Court are a key element in the reform of the rule of law in Bosnia-Herzegovina," Ashdown said.
"Bosnia-Herzegovina has decided to ensure the effective processing of war crimes cases through the domestic legal system -- to fail in this regard would be a very negative signal," del Ponte underlined.