Foreign Minister Mustafa Osman Ismail reiterated on Wednesday in Khartoum the government's rejection of trials of its nationals abroad but said: "We seek a balance between the red line that the Sudanese people have set and the implementation of the resolution in cooperation with the ICC.
"The law of the court gives Sudan the opportunity to try the suspects in Sudan."
The UN Security Council on 31 March voted to refer a sealed list of 51 people accused of crimes against humanity in Darfur to the court in The Hague, after allowing exemptions for US citizens.
Security Council diplomats in New York said the court had stepped in because Sudan had failed to prosecute those responsible for mass crimes against civilians.
Thousands of people in Darfur, in Sudan's west, die each month from violence, hunger and disease, and more than two million have been herded into squalid camps.
Most atrocities are blamed on pro-government Arab militia fighting a rebel uprising.
Ismail on Wednesday denied reports that a senior Sudanese leader was on the UN's list of 51 Darfur suspects.
Support for resolution
A Sudanese opposition leader, speaking to Aljazeera by telephone from Paris on Thursday, urged the government to respect the Security Council resolution.
Sadiq al-Mahdi, leader of the Umma Party, said, "Sudan's government should abide by the resolution for the International Criminal Court to try criminals."
He said the government lashed out at the party, in a raid on its headquarters in Omdurman on Wednesday, because of its stance on the Darfur trials.
"There was a connection between suspending the party's legal status and the party's position toward the UN resolution about Darfur."