But Mohammed Ali al-Mardi, Sudan's justice minister, said on Tuesday: "We are not concerned with, nor do we accept, what the ICC prosecutor has opted for.
"Our position [on handing over any indictees] remains the same."
Haroun told Al Jazeera that the ruling was politically motivated.
Haroun, a former state interior minister, and Abd al-Rahman, a militia commander also known as Ali Kushayb, are the first two suspects to be sought by the ICC.
Al-Mardi confirmed that Abd al-Rahman has been in detention in Khartoum since November on suspicion of violating Sudanese laws and was under investigation for actions in Darfur.
Sudan has repeatedly said it will not respect any indictments handed down by the ICC, and it is not a signatory to the convention that created the international court.
The court said the two were suspected of war crimes and crimes against humanity including rape and murder.
Haroun and Abd al-Rahman were part of a conspiracy to "persecute civilians they associated with rebels," Moreno-Ocampo said.
The UN Security Council in March 2005 had asked the ICC to launch an investigation into the violence in Darfur, which the US has called genocide, a charge Khartoum denies.
Osman Hummaida, a Sudanese human rights lawyer, said: "We eagerly await the prosecutor's recommendations for holding those responsible for the gravest crimes fully accountable."
Haroun told Al Jazeera that the ICC had "no jurisdiction to take action on this issue for the simple reason that the government of Sudan did not approve the ICC basic law".
"The real issue is not a legal one, it is purely political," he said.
"When [Moreno-]Ocampo becomes able to try those who bomb children and innocent people beyond their borders, such as [US President George] Bush and [former Israeli prime minister Ariel] Sharon, we would consider standing for trial before the ICC. This is part of a psychological warfare where double dealing is an accepted norm.
"Ironically, those who carry arms against the state and terrorise innocent people in the Sudan and elsewhere, would be branded as heroes, while those who perform their duties by countering them, should face baseless charges.
Analysts say about 200,000 people have been killed and 2.5 million others driven from their homes in Darfur since 2003, when rebels took up arms against the government, charging it with neglect. Khartoum says about 9,000 people have died.
Richard Dicker of Human Rights Watch based in New York said: "I hope the message that goes out from this action is that the days of absolute impunity that have existed for horrific crimes committed in Darfur are coming to an end."
UN and African Union observers blame pro-government militias, known as Janjawid, for the worst atrocities.
Sudanese media reported that Khartoum would put several people on trial next week, including military personnel and paramilitary troops, for suspected involvement in attacks in Darfur.
Moreno-Ocampo has said he would examine whether Sudan's government is conducting its own judicial proceedings over Darfur as the ICC is only supposed to prosecute when national courts are unwilling or unable to act.
Rights groups say Khartoum's own investigations and tribunals for crimes in Darfur have been largely for show.
The ICC, the world's first permanent war crimes court, started work in 2002 and is now supported by 104 nations, although still not by Russia, China and the US.
Washington fiercely opposed the creation of the ICC, fearing it would be used for politically motivated prosecutions of its citizens.
But Washington has refrained from blocking Darfur's referral to the ICC.