Sudan's agriculture minister and head of the Sudanese government delegation to the Darfur peace talks described the move as unacceptable.
"If the International Criminal Court wants to carry out observation tasks, in cooperation with the Sudanese judicial authorities, in order to feel relieved and certain, the Sudanese government has no problems or objections," Majdhub Khalifa said.
"However, if it wants to begin any procedures to try Sudanese citizens, this is unacceptable," he added.
The rebel Sudan Liberation Movement (SLM) in Darfur slammed the government's rejection, saying it represented a threat to peace talks, due to be held in Abuja on Friday.
The movement has issued a statement saying that Khalifa's announcement has destroyed the negotiations before they even start.
The SLM says the government's
stance is a threat to peace talks
The movement is ready to supply the international investigator with documents that prove the government's involvement in Darfur crimes, the statement added.
The ICC on Monday formally launched an investigation into alleged war crimes in Darfur, where tens of thousands have been killed and more than two million forced from their homes during more than two years of uprising.
Meanwhile, all parties to the Darfur peace talks will attend the next round of African Union-sponsored negotiations after a six-month lull.
Khalifa said his delegation would be in the Nigerian capital Abuja in time for the planned start of talks on Friday.
"We are ready to go to Abuja for negotiations hoping to reach a final settlement for the case of Darfur and we'll be there on time on the 10th of this month," Khalifa said.
Darfur's two main rebel groups, the SLM and the Justice and Equality Movement (JEM), have also expressed their willingness to attend.