The continued freedom of the two men wanted over the Srebrenica massacre is an obstacle to peace in Bosnia, the UN High Representative has said.
Paddy Ashdown has been the effective ruler of Bosnia for three years
Paddy Ashdown said the failure to arrest General Ratko Mladic and Bosnian Serb leader Radovan Karadzic was mainly the fault of the Serbian authorities.
However, he noted that they had now begun to co-operate with The Hague war crimes tribunal.
Lord Ashdown is stepping down from his job after three years.
In an interview with BBC Radio 4's Today programme, he said the arrests of Mr Mladic and Mr Karadzic were crucial to the future of Bosnia.
"It's a frustration and it's a failure not to bring these people to The Hague," he said.
"You can not have peace without justice, that's a piece of unfinished business that has to be done.
"It might be done, I suppose, before I leave, but I think that a little unlikely.
"But we will continue to push for this to happen, and we need to recognise that the job of stabilisation in Bosnia and Herzegovina is not done until justice is established.
"And justice is not established until these two people are in The Hague."
Lord Ashdown was upbeat about Bosnia's future, noting that it had recovered sufficiently to be considered a serious candidate for membership of the European Union.
He nonetheless admitted that in many ways, Bosnia remained a "dysfunctional state" propped up by international peacekeeping initiatives.
But comparing Bosnia with other conflict areas such as Northern Ireland and Cyprus, he said: "The miracle of Bosnia is that it's come so far so fast."
The Bosnian civil war was the bloodiest conflict in Europe since 1945, with the killing of thousands of Muslim men and boys from Srebrenica in 1995 a low point.
The town was supposed to be a safe haven under UN protection.
As the International High Representative in Bosnia, Lord Ashdown has sweeping powers that date back to the Dayton peace accords signed 10 years ago.