From the Jewish hillside cemetery, where Jakob Finci's ancestors lie buried, the sightlines down into central Sarajevo are clear. It is easy to see why it became a strategic post for Bosnian Serb gunners and snipers as they surrounded the city with a ring of firepower in April 1992, at the start of the longest siege of a major city in modern history.

It was Finci's charity, Benevolencija, that spearheaded early efforts to get medical supplies to the population, and it eventually became the only local organisation delivering humanitarian relief on a non-sectarian basis. Few dared approach the Serb checkpoints for fear of summary execution. But Benevolencija found a way to get people out, by organising mixed convoys of Muslim, Croat and Serb families.

"We somehow managed to get clearance from all the parties," Finci tells me, shaking his head as if he still doesn't quite believe it. "We got permission from the Bosnian government for people to leave, negotiated safe passage from the Serbs, and entry to Croatia." In all, they got more than 3,000 people to safety.

After the war ended with the US-brokered Dayton peace agreement, Finci became one of Bosnia's most respected public figures. He was elected to chair a national committee charged with setting up a truth and reconciliation commission, and was appointed head of the civil service agency. But his political career was eventually blocked, in such a devastating fashion that he has now taken his own government to the European court of human rights. For under the Dayton constitution, Finci is barred from standing for the Bosnian parliament's upper house or the presidency for one simple reason: he is a Jew.

Of the community of Sephardi Jews who had first settled in Sarajevo in the mid-16th century, most did not survive the second world war. Finci himself was born in 1943 in an Italian concentration camp. After Italy's armistice with the Allies, the newborn Jakob was evacuated with his parents.

Then, in 1991, war returned to the Balkans. Benevolencija had been an old Jewish cultural and welfare organisation, and it was re-established in Sarajevo with Finci as vice-president. As the conflict spread from Slovenia to Croatia, they managed to get medicine through to a small group of elderly Jews trapped in besieged Dubrovnik. Finci wags his finger: "We learned our lesson. Back in Sarajevo, we started to stockpile medicines and later food – tinned food, pasta, rice, oil – enough to last a winter." When the first shots were fired in the Bosnian war in April 1992, they immediately organised the first evacuation of children and the elderly. Half of the 1,400-strong Jewish community left, "but many said they could not run again".

When the former Bosnian Serb leader Radovan Karadzic went on trial in The Hague recently, the prosecutor described Karadzic's vision of a greater Serb republic carved out of an ethnically divided Bosnia. On the eve of the war, Karadzic had warned: "Sarajevo will be a karakazan, a black cauldron, where 300,000 Muslims will die . . . Europe will be told to go fuck itself, not to come back until the job is finished."

"At the start of the siege of Sarajevo, everything was looted," Finci says. "But we still had more drugs than we needed because most of our elders had left. As we had always lived with the other communities, we decided to share everything with them." Benevolencija opened a free pharmacy, which eventually supplied more than 40% of the medical needs of the population. "People used to say, 'If you can't find it in the Jewish pharmacy, it isn't in Sarajevo,'" says Finci proudly.

Benevolencija also opened a soup kitchen, serving 300 hot meals a day, seven days a week, for anyone who turned up. It also began a Sunday school for 20 Jewish kids. Finci smiles and says, "One boy would ask if he could bring along his best friend, and we soon ended up with 50 'best friends' from all the different communities. We taught them about living together."

Benevolencija's Jewish identity made it acceptable to Bosnian Muslims, Serbs and Croats alike, and also constituted a token of neutrality in the negotiations to evacuate people from the city. Finci recalls wryly the "new Jews" who appeared, people who suddenly discovered their Jewish heritage. He also remembers one Muslim couple who turned to him for help when they couldn't get out. "My own parents had died years before, but their ages were about the same. So I dug out some old documents to give to the couple – now the records show that my mother and father left Sarajevo during the siege."

The 1995 Dayton peace agreement was regarded as a coup for American diplomacy and a personal triumph for the chief negotiator, Richard Holbrooke. When the leaders of the three main communities couldn't agree who would control a particular institution, Holbrooke's solution was to give them one each. The state of Bosnia and Herzegovina now has two territories, the Republika Srpska and the Bosniak-Croat Federation, three prime ministers, and a rotating three-person presidency. Membership in the upper house of parliament is reserved for equal numbers of Bosnian Muslims, Croats and Serbs. Other groups, including Jews and the Roma, are effectively excluded from the highest offices.

Finci says that he met Holbrooke several times, both before and after Dayton. "I asked him why I couldn't stand for election like everyone else. He said, 'This is nothing against you, but it was the first thing the three agreed on – to share power.'" Holbrooke is now President Obama's envoy to Afghanistan and Pakistan.

Minority Rights Group International has supported Finci in bringing a case to Strasbourg for breach of the European convention on human rights. The court ruled at the end of last year that no exclusion based "on a person's ethnic origin is capable of being objectively justified in a contemporary democratic society". The judgment effectively requires the constitution be amended before an electoral deadline at the end of this month, and comes at a critical time for Bosnia as it seeks to join the EU.

But earlier attempts to reform the constitution failed to get agreement from the different groups. Paddy Ashdown, the international community's high representative for Bosnia and Herzegovina until 2006, likes to point out that Dayton was a good agreement to end a war but a bad agreement to build a state. Fracturing power between the three peoples has left state institutions feeble and at the mercy of a system of vetoes, while creating electoral incentives for politicians to appeal to narrow nationalist sentiments.

When I spoke to Ashdown recently, he was frustrated at the EU's failure to insist on reform. He says the Bosnian Serb leadership is trying to sabotage the country's political unity and reform of the constitution in order to secure effective independence for the Republika Srpska. "Europe is sweeping the problems under the carpet, just as we did in 1992. The EU will be left with a black hole of corruption and a dysfunctional state in the heart of Europe, or the country will split apart. And we will be caught twiddling our thumbs while the policy of Karadzic comes to pass."

Finci is more optimistic about Bosnia's multi-ethnic future. But he says: "The constitution we have now is not good enough – we need to have equal rights for all. Roma and Jews are not second-class citizens."

He thinks some 40% of the Jews who fled the siege returned after the war. He currently serves as Bosnia's ambassador to Switzerland, and is still president of Benevolencija, now running a large cross-community programme for isolated elderly people.

"I am the first member of my family in 350 years not born in Sarajevo. But I hope I won't be the last to be buried here." His two sons live in the US, and he knows he has to let them decide for themselves. But the old Jewish cemetery, damaged by shelling and then mined, has been restored. Finci's own parents returned with him to Sarajevo after the second world war. He shrugs.

"When Israel was founded, many talked of emigrating, but my parents didn't want to go. They said, 'We just came home.'"

• Mark Lattimer is director of Minority Rights Group International