Harun is the minister responsible for providing humanitarian assistance in Darfur and Kushayb, a leader of the Janjawid militias.
Both face a list of 42 and 50 charges of crimes against humanity and war crimes respectively allegedly committed in West Darfur in 2003 and 2004.
Harun was exonerated by an official Sudanese commission following investigations of his tenure.
Kushayb was detained last year on the basis of other charges being brought in national proceedings but the opening of his trial was postponed indefinitely.
Richard Dicker, head of the International Justice Programme of New York-based Human Rights Watch, said Sudan risked further isolation "if it shelters suspects indicted for crimes against humanity in Darfur".
The ICC's appeal to the Security Council comes as the world community cranked up pressure on the government to agree on the deployment of a 23,000-strong joint force in Darfur.
Zalmay Khalilzad, the US ambassador to the UN said Khartoum should quickly accept the deployment or face UN sanctions, including the imposition of a no-fly zone over Darfur.
He also urged the government to co-operate with the ICC prosecutor in handing over the two alleged war criminals.
The US, UK and France have threatened to tighten sanctions if Sudan does not resolve the Darfur conflict quickly.
The US imposed stricter trade and financial sanctions on Sudanese companies while threatening to press for broader UN economic sanctions on the country's leaders, expand an arms embargo on Sudan, and impose the no-fly zone over Darfur.
The Darfur conflict began in 2003 after an ethnic minority uprising against the Arab-dominated government, which then enlisted the Janjawid militias to help crush the rebellion.
The government said 9,000 people have died, but the UN estimates at least 200,000 people have died and more than two million made homeless.