Previously, it had insisted that Serbia must first arrest General Ratko Mladic, indicted by the war-crimes tribunal.
Serbia was engulfed by unconfirmed rumours that Ratko Mladic , the wartime Bosnian Serb general, had been arrested.
Burns suggested that the military leaders, Ratko Mladic in particular, are hindering compliance.
Judges said the former intelligence chief was the "right hand" of Ratko Mladic, also on trial at The Hague.
Among them are Radovan Karadzic, the former president of the Bosnian Serbs, and Ratko Mladic, once their military chief.
Ratko Mladic announced that relations with NATO were being severed because of the detention of two Bosnian Serb army officers.
Ratko Mladic has been indicted for war crimes and should surrender his office under the terms of the Dayton peace accord.
CNN: Bosnia talks founder as key Bosnian Serb fails to turn up
But the NATO secretary general said that would not change Alliance tactics, only Bosnian Serb General Ratko Mladic can do that.
The most important is Ratko Mladic, who led Bosnian Serb forces during the war and is believed to be hiding somewhere in Serbia.
ECONOMIST: More arrests and court cases revive bad Balkan memories
Zdravko Tolimir, a close aide to Bosnian Serb commander Ratko Mladic during the Bosnian War, is accused of war crimes at the international tribunal at The Hague.
The Bosnian Serb leader, Radovan Karadzic, and his military chief, Ratko Mladic, were still at large at the end of her tenure, though Mr Karadzic has since been arrested.
Serbia's hopes of joining the EU were for many years frozen pending the capture of two of the Bosnian war's most high-profile war crimes suspects, Radovan Karadzic and Ratko Mladic.
His arrest means that General Ratko Mladic, the Bosnian Serbs' former army commander, is the only major alleged war criminal indicted by the court who is still at large, at least occasionally, in Serbia.
More important still, it might give him political cover to do the unthinkable: to order the arrest of the two big fish still at large, General Ratko Mladic and Radovan Karadzic (if either is in Serbia).
Serbia's path to becoming an EU candidate was given a boost last year when two major war crimes suspects - former Bosnian Serb commander Ratko Mladic and former Croatian Serb leader Goran Hadzic - were arrested.
Both organisations will be involved in the apprehension of war criminals, believing that combined assets will make it easier to capture those still on the run, including the former Bosnian Serb leaders Radovan Karadzic and Ratko Mladic.
Until now, however, it was believed that Mr Karadzic and his wartime military commander, General Ratko Mladic (who remains at large, for now), were protected by powerful networks of former or current members of the security services.
But one issue he was unable to resolve and one which his successor will face is the continued freedom of the two former Bosnian Serb leaders, Radovan Karadzic and Ratko Mladic, who have been indicted for war crimes.
One problem is that this process cannot be completed without the arrests of Radovan Karadzic and Ratko Mladic, the Bosnian Serb wartime leaders, who are still at large a decade after having been indicted by the Yugoslav war-crimes tribunal.
Like the lightly-armed Dutch contingent of U.N. peacekeepers in Srebrenica, brushed aside by Bosnian Serb forces commanded by General Ratko Mladic, the 300 U.N. monitors in Syria have no power to influence events -- just to observe and report them.
CNN: Syria, Sarajevo and Srebrenica: When outrage isn't enough
SARAJEVO, Bosnia-Herzegovina (CNN) -- As pressure mounts for someone to save the faltering Bosnian peace process by arresting indicted war criminals Radovan Karadzic and General Ratko Mladic, the two continue to run 49 percent of Bosnia as an ethnic separatist state.
By nightfall, NATO jets were roaring over Sarajevo on surveillance and close air support missions, but the U.N. was receiving mixed messages -- a five page long letter from General Ratko Mladic that the U.N. said was unacceptable and a short terse note from Bosnian Serb political leaders saying they would comply.
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