BELGRADE, Sept 21 (Reuters) - U.N. prosecutor Carla del Ponte ended a visit to Serbia on Friday to determine whether Belgrade is doing its best to capture suspected war criminals, a key to its European Union future.

The EU and Serbia wrapped up technical talks last week on a Stabilisation and Association Agreement (SAA), the first step to eventual EU membership, but before signing, Brussels wants Del Ponte's assurances on Serbia's efforts to arrest the fugitives.

The four remaining suspects are all ethnic Serbs. The most wanted among them are Bosnian Serb general Ratko Mladic and his political boss Radovan Karadzic, both charged with genocide.

Independent radio station B92 quoted government sources as saying del Ponte's report "will not be negative" and after hours of talks she was convinced authorities were searching seriously.

"Allegedly, that's why she won't oppose Brussels initialling the SAA with Belgrade, but will insist on conditioning it with full cooperation with the Hague (war crimes) court," B92 said.

Daily "Blic" said she asked specifically about the handover of fugitives Goran Hadzic and Stojan Zupljanin, who are seen as smaller fish and easier to arrest.

In her eight years as chief U.N. war crimes prosecutor, she has come to Belgrade a dozen times, mostly berating governments for protecting or failing to look for fugitives, but praising them after arrests.

Her recommendations resulted in the freeze of Serbia's talks with the EU in 2006, and their resumption in last June. With her term ending on Dec 31, she has urged Brussels to be firm with Serbia, and not let politics override justice.

"It is in Serbia's interest to finish cooperation with The Hague as soon as possible," Prime Minister Vojislav Kostunica's office said in a statement after his meeting with del Ponte. There is a "strong political will and determination" to do it.

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