One of the most frightening aspects of the crime of genocide, war crimes or crimes against humanity is not so much their scale as their relationship with the sovereign power of the state, which either condone, or even participate in their making. It happens when the theoretically unlimited sovereign state power, which is connected with a monopoly on the use of coercive measures, begins to be used against its own citizens. Because of such a misuse of the state functions in the second half of the 20th century international law began to be treated as an element of protection of innocent people against the unpredictable sovereign state. Providing such a protection is enshrined in the international conventions, and in the activities of various international bodies, including in particular the Security Council of the United Nations. But so far there has not been found in the international law an ideal way to solve the conflict between the need to protect fundamental individual rights and the respect of sovereignty of the state. Creation by an international treaty of the International Criminal Court can be described as a major step on the way to the final determination of the relationship between human rights and state sovereignty. Hence, the process of its creation and first years of operation was marked by a dispute between the defenders of those values. In particular this is reflected in a controversy that caused the issuing by the Court of the arrest warrant for the Sudanese President Omar al-Bashir, suspected of committing on the territory of Darfur war crimes, crimes against humanity and genocide. One of the key issues emerging in connection with the Arrest Warrant issued for the head of state is a way to determine the mutual relationship between the obligations of states towards the international court, appointed for the purpose to prevent the gravest international crimes remaining unpunished, and the norms of international law obligating respect for the state sovereignty, by ensuring the immunity of his head is being observed. This article is an attempt to analyze this relationship, regarding the provisions of the Statute of the International Criminal Court, the wording of Security Council Resolution 1593, refering to the Court situation in Darfur and the Security Council Resolution 1970 refering to the Court situation in Libya, and also appropriate rules of customary international law and decisions of international courts.