"There was a country ready to receive the plane once it was diverted, but he was tipped off and got off the plane. So he never went to Mecca."
Olara did not name the countries that were involved in the operation and gave no further details on the plan.
However, she said that Saudi Arabia was aware of the ICC operation.
Riyadh, which is not a signatory to the ICC statute, would not have been legally obliged to arrest Harun if he had arrived there, experts in international law have said.
Speaking in Khartoum, Harun told Al Jazeera that the ICC had revealed itself to be a group of "pirates, terrorists and criminals".
"First, it seems that this unrespectable court acts in a criminal way ... Second, this court is unrespectable as it does not search for the truth, but keeps lying. The evidence to this is that I have not intended nor planned to perform Hajj.
"I was busy with the activities of the six-party committee which was working on resolving the political crisis in the country at that time.
"The third proof that discloses the lack of this court's information is its primitive vision towards the situation in Sudan. We are a respectable country."
Harun said Sudan does "not accuse any specific country" of involvement in the ICC plot, which he called "an attempt to spark strife".
The ICC issued arrest warrants for Harun and Ali Kushayb, a Sudanese militia commander, in April 2007.
They are wanted on 51 counts of crimes against humanity and war crimes, including incitement to murder, rape, torture, and the forced displacement of civilians in the western region of Darfur.
Earlier this week, Sudan said it would not answer the ICC's call that the two men be handed over.
At least 200,000 people have died and 2.5 million have been driven from their homes in Darfur since a rebellion erupted there five years ago, experts have estimated.
Khartoum dismisses the figures, saying that 10,000 people have died in the region.
Luis Moreno Ocampo, the chief ICC prosecutor, told the UN Security Council on Thursday that he would seek more indictments next month against Sudanese officials.
He said that Khartoum's "entire state apparatus" was involved in crimes perpetrated in Darfur.
The Sudanese government has been accused of having direct links to Arab janjiwid militia responsible for atrocities in Darfur.
Khartoum denies any such relationship.