Hoon, who arrived from Zagreb, held talks with Serbia and Montenegro President Svetozar Marovic and Defence Minister Prvoslav Davinic.
He told the press it was imperative that war crime indictees be transferred to The Hague so that they could be appropriately tried.
Hoon said Great Britain would continue to support the state union's defence reform so that Serbia and Montenegro could prepare for membership in a broader Euro-Atlantic community.
The defence secretary said Great Britain wanted to see Serbia and Montenegro in NATO and its Partnership for Peace programme, as well as in the European Union, but was aware that it took time.
Hoon said his country wanted the whole region to be part of a broader European context, in which he added finding a solution to the Kosovo issue was vital.
President Marovic said the authorities in Belgrade were aware that the speed at which Serbia and Montenegro would join Partnership for Peace and other Euro-Atlantic structures depended on cooperation with the Hague tribunal.
"We reiterated that cooperation with the Hague tribunal is our obligation and that we don't expect someone else to do it for us. We only expect understanding for the political delicacy, but we assured our friends in Great Britain that we are determined to see this job through, in the interest of Serbia and Montenegro's European future," Marovic told the press after the talks.
He added the Kosovo issue "can be settled only the European way," which he said meant the creation of conditions for a free and safe existence for all Kosovo residents. He added this could be achieved through political dialogue among Kosovo's political representatives, Belgrade-Pristina dialogue, as well as dialogue among all countries of the region, because the Kosovo issue was important for the region's stability and future.