Williamson's first visit to Sarajevo came after visits to Serbia and Croatia.
The Bosnian Presidency said in a statement Williamson also informed Tihic of the US government's assessment that nowhere in the world were war crimes so much linked and intertwined with the political and security situation as in this region, and that this was why those issues must be settled.
Williamson said regional cooperation was the best way to arrest Radovan Karadzic and Ratko Mladic, and supported the development of domestic judicial capacities so that all remaining war criminals could be tried.
Tihic said the Hague tribunal must not close its doors before Karadzic and Mladic were arrested. He also called on the US administration to support the tribunal's incumbent chief prosecutor, Carla Del Ponte, saying she was doing her job well.