The more militant group, based primarily around the divided northern town of Mitrovica has taken advantage of its numerical strength and has been largely successful in preventing the return of ethnic Albanians to the northern part of the town.
Kosovo's ethnic Serb community - which was estimated to number close to 200,000 on the eve of last year's conflict - has gone down by about half since Serbian security forces were obliged to pull out of the province at the end of Nato's 11-week bombing campaign.
No one knows the exact figures for those who fled revenge attacks by Kosovo's ethnic Albanian majority since the war ended a year ago.
But it is reckoned that around 100,000 Serbs and tens of thousands of other non-Albanians - mostly Roma, Muslim Slavs and Montenegrins - have left Kosovo for the safety of Serbia, Montenegro and Bosnia-Hercegovina.
Serb divisions
Within Kosovo itself the ethnic Serb community is split into two parts.
The more militant group, based primarily around the divided northern town of Mitrovica has taken advantage of its numerical strength and has been largely successful in preventing the return of ethnic Albanians to the northern part of the town.
This could not have been achieved without a protective ring of K-For peacekeepers who want to prevent further inter-ethnic conflict.
"The whole concept of the protection of Mitrovica and the survival of the people in this area is based on the self-organisation of the local population. When this is achieved, KFOR can provide added protection," Mr Ivanovic says.
Milosevic support
The Mitrovica leadership is believed to be close to President Slobodan Milosevic's administration in Belgrade from where it has been receiving considerable support over the past year.
It has also eschewed co-operation with the UN administration (Unmik), arguing that the new power-sharing bodies and the forthcoming municipal elections are paving the way for Kosovo's independence - the Kosovar Albanians' 10-year-old objective.
By contrast, the Serb leadership around Bishop Artemije, which is centred on the small monastery town of Gracanica, just outside Pristina, has been more willing to work with Unmik.
But recently the Gracanica-based Serbian National Council announced it was suspending its participation in the Interim Administrative Council because of the latest acts of violence against Kosovo's remaining Serbs.
This temporary suspension is an indication of its generally ambivalent position.
That, in turn, is linked to the extremely difficult conditions in which it has to operate.
Caught in a bind
Unlike in Mitrovica, where there is a sizeable concentration of ethnic Serbs, the Gracanica leaders are trying to look after a large number of small Serbian communities dispersed over wide areas of Kosovo.
They are on bad terms with the Milosevic regime which they have accused both of introducing repressive measures in Kosovo and of betraying the interests of Kosovar Serbs.
In the face of continuing violence at the hands of Kosovar Albanian militants, the Gracanica group can only look to the UN and the K-For peacekeepers for protection.
Yet the international bodies can barely provide sufficient security sometimes even for their own staff.
Mr Kouchner has just announced the closure for eight days of a Kosovar Albanian paper, Dita, which recently named an ethnic Serb staff member of Unmik as a war criminal - an action that almost certainly led to his subsequent murder.
And when that protection proves inadequate, they feel badly let down.
Doubts about UN
The Gracanica Serbs have had serious doubts about Unmik's intentions and effectiveness.
It was only two months ago they joined the Interim Administration Council that had originally been formed in January.
And even when their representative did start attending its meetings in April, it was initially only on a trial-period of three months and only as an observer.
Now the Gracanica leaders feel once again let down following the latest spate of killings.
They are taking their case to the UN Security Council, as it reviews the first year of UN administration in Kosovo.
Whether the moderate Serb representatives can obtain the additional security guarantees they want - let alone get greater protection on the ground - remains to be seen.
But given their weak position, it's unlikely they have any viable alternative to working hand-in-hand with Unmik.