"The council of ministers has reached a conclusion that the resolution is contradicting justice and objectivity and violating national sovereignty," Information Minister Abd al-Basit Sabdarat said on Sunday after a cabinet meeting chaired by President Umar al-Bashir.
He added the resolution was "a political one that is unrelated to the law and will not contribute to resolving the Darfur problem but will, rather, give the rebels a wrong signal to continue with their stubbornness."
The Security Council voted on Thursday 11-0 to refer Darfur suspects to the International Criminal Court, two months after an international enquiry found evidence of war crimes in the region, where an estimated 300,000 have died in two years of violence.
The move clears the way for the Hague-based court to prosecute those behind the murder, rape and pillaging in the country's western Darfur region, after weeks of tense diplomatic haggling over how to bring the guilty to justice.
Sabdarat said the cabinet would launch "an extensive diplomatic campaign" to clarify its position and had instructed the legal authorities to "continue with their duties" of investigating violations of human rights and other war crimes.
"No impunity will be granted to any person or official who proves to be involved in Darfur crimes," Sabdarat said.
"We have refused handing over the suspects because we are convinced of the competence of the Sudanese judiciary for trying them."