The fact that Radovan Karadzic will face trial has important ramifications for the case against Omar Bashir, which must not now be delayed. Most obviously, the arrest of Radovan Karadzic is good news for the victims of the Bosnian war and their relatives. As one woman in Srebrenica said this week: "Justice is achievable, after all." But this remarkable moment has a broader historic importance, too.

The expected delivery of the former Bosnian Serb leader to the war crimes tribunal in The Hague is part of Serbia's coming to terms with its role in Bosnia's war, where Belgrade played a key role in a campaign of ethnic cleansing that included the genocide at Srebrenica. It helps not just with possible future membership of the European Union, but also moves Serbia towards a better understanding of its own recent history, and thus a greater stability. Crucially, too, the arrest has significance well beyond the Balkans – most obviously and immediately, in Sudan.

The arrest of this European politician, charged with genocide and crimes against humanity, comes just days after the request from the prosecutor of the international criminal court for an arrest warrant against the Sudanese president, Omar Bashir. There are many differences between the two cases. But the parallels are striking, too.

Western politicians were initially reluctant to bring to justice those who presided over the crimes in Bosnia, just as some are now reluctant to see Bashir indicted. They preferred to shuttle Karadzic and his patron, Serb leader Slobodan Milosevic, to and from talks in luxurious hotels in Geneva, London and elsewhere. Milosevic needed wars to stay in power, so that's what he did. First came a small war in Slovenia in 1991; then a larger one in Croatia; then a still larger war in Bosnia, which lasted from 1992 to 1995; and, finally, a war in Kosovo in 1999, which proved his downfall. (In Sudan, the crimes committed in the long war between north and south – including village burnings, rape, ethnic cleansing and mass murder – partly prefigured the crimes committed in Darfur.)

Understandably, Karadzic and Milosevic were confident that they would never face justice. They lied with cheerful brazenness. As a journalist covering the Balkans, I asked Karadzic about the snipers surrounding the besieged city of Sarajevo, who exposed civilians to the daily risk of death. There were "no Serb snipers", Karadzic told me. All the killings were organised by Muslims, to gain sympathy for their cause. Milosevic was more brazen still. When I asked him about the possible creation of a war crimes tribunal, already in discussion in the early months of the Bosnian war, he was enthusiastic: "If any citizen of Serbia is involved in any crime, he will be the subject of criminal prosecution." He looked astonished when I dared to suggest that he might find himself on such a list one day. No, no: he was "for peace". Bafflingly, western politicians believed him.

When the indictment of Karadzic was announced in July 1995 – shortly after the Srebrenica massacre, in which thousands were massacred in cold blood – many argued that this was the wrong moment to seek his arrest. By the "wrong" moment, they meant, of course, that any moment for justice was wrong.

A few years later, some made the same argument with regard to the Chilean dictator, Augusto Pinochet. Prosecuting Pinochet could destabilise Chile at this difficult moment in the country's history, they said. In reality, the opposite proved to be the case. The more the Chilean courts stripped Pinochet of his diplomatic immunities in the next few years, the more Chile became a successful and stable democracy.

And now, the same argument about stability is again heard, with respect to Bashir. The argument is as misguided now as it was before.

Some governments want the United Nations security council to second-guess the independent prosecutor in this case, stemming from the first-ever situation that the security council itself referred to the international criminal court, in 2005. They want the security council to order the prosecutor to put the case against Bashir on hold – especially if Sudan can be persuaded to avoid criminal behaviour for the next few months. And yet, in Sudan, as in the Balkans, justice put to one side means justice denied.

If the arrest warrant against Bashir is confirmed by the ICC judges that will be a gift to the people of Darfur, and to those who wish for a better Sudan. Conversely, giving Bashir a free pass as a reward for the prospect of a few months' good behaviour would be a travesty – just as it was a travesty when some politicians wanted to leave Karadzic alone, more than a decade ago, or wanted to leave Milosevic alone, in 1999.

In the Karadzic case, justice now looks set to be done. It will be equally essential to allow Luis Moreno Ocampo, the independent prosecutor of the ICC, to do his job without political interference. That means allowing the case against Bashir to go ahead if confirmed by the judges – with no ifs, and no buts. The Serbs have shown the way. One day, the Sudanese can follow.