THE HAGUE — Western governments have begun private talks aimed at coming up with fresh strategies to speed the process of judging those responsible for grave crimes in the conflicts in Syria and Iraq.

Some governments have already been paying various groups to collect evidence of crimes in Syria since 2012. Now, spurred on by the recent escalation of violence by the Islamic State terrorist group, they are discussing ways to use national and international courts in anticipation of the capture of important suspects, diplomats said.

The cases cannot go to the International Criminal Court because neither Iraq nor Syria is a party to it. A prosecution there would require a referral from the United Nations Security Council, which is unlikely.

The next step in the talks will take place at the Dutch Mission to the United Nations in New York on Wednesday, coinciding with this year’s General Assembly debate.