Mr Haroun, currently Sudan's humanitarian minister, was state minister for the interior of Sudan and head of the 'Darfur security desk' at the time of the accusations levelled against him.
It is alleged he liaised with Mr Kosheib, leader of the janjaweed militia, to encourage government-backed troops into "attacking civilians and pillaging towns and villages".
Prosecutor Luis Moreno-Ocampo said: "We completed an investigation under very difficult circumstances, from outside Darfur, and without exposing any of our witnesses.
"We transformed their stories into evidence, and now the judges have confirmed the strength of that evidence."
ICC regulations state that it should only act when national courts are unwilling or unable to investigate or prosecute such crimes.
Khartoum has previously asserted its right to prosecute all internal cases without international intervention, but Mr Moreno-Ocamp rejects this argument.
"The judges have issued arrest warrants. As the territorial state, the government of… Sudan has a legal duty to arrest Ahmad Harun and Ali Kushayb," he said.
"This is the ICC's decision, and the government has to respect it."
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