In a separate opinion, one of the three judges, Marc Perrin de Brichambaut, raised an argument that may open new legal avenues for rights activists. The judge said that South Africa and Sudan were both obliged to arrest Mr. Bashir because they had both signed the United Nations genocide convention, which took effect in 1951. Some 147 countries have ratified that treaty, nearly two dozen more than have joined the International Criminal Court.

Mr. Bashir has been accused of genocide involving three tribes in the Darfur region of western Sudan. The charges cover violence that erupted there in 2003 when Mr. Bashir ordered a counterinsurgency in the conflict between his Arab-dominated government and non-Arab rebel groups.

According to prosecutors, government militia gangs backed by military and police helicopters looted and burned hundreds of villages, bombed schools, poisoned wells and engaged in systematic rape of women and girls. The United Nations estimates that about 300,000 people died and more than two million were driven from their homes.

The court ordered Mr. Bashir in 2009 to face charges of war crimes and crimes against humanity, and judges added the genocide charges later.

Mr. Bashir has tried to enlist other countries in a campaign against the court, but he has never found enough backing on the Security Council to get the case against him dropped.

Three other Sudanese officials are also the subject of warrants from the court: a former minister of humanitarian affairs, Ahmad Muhammad Harun; a militia commander, Ali Kushayb; and a former defense minister, Abdel Rahim Muhammad Hussein.

Mr. Bashir has made a point of traveling in Africa and Asia to demonstrate that he commands some sympathy in the world. But he has had to avoid the United States, Western Europe and other places where he might be arrested. Some countries, including Turkey and Saudi Arabia, have quietly disinvited him; in others, leaders have maneuvered to avoid appearing in official photographs with him. He disappeared suddenly from an official luncheon in Nigeria, where he was scheduled to speak, after getting word that local lawyers were seeking his arrest.