Speaking to an army garrison in the southern province of the country, the official news agency Suna quoted al-Bashir as saying the state would not hand over any suspects for trial outside the country.
Al-Bashir also said while visiting the Bahr al-Ghazal province on Saturday that Sudan's judicial system would take charge of any prosecutions.
A UN Security Council resolution at the end of March empowered the court to prosecute alleged perpetrators of war crimes in Sudan's Western Darfur region.
Fifty-one Sudanese suspects were identified by a UN inquiry commission sent to Sudan to assess human rights abuses.
Arab League involvement
Meanwhile, Arab League Secretary General Amr Musa, speaking to Aljazeera, said consultations were under way to deal with the Security Council resolution referring suspects to the International Criminal Court (ICC).
Musa held meetings in Cairo with the Sudanese Foreign Minister Mustafa Usman Ismail on Saturday, discussing all aspects regarding the Security Council resolution, he said.
For his part, Ismail railed against UN Secretary General Kofi Annan, accusing him of turning the international body into "a megaphone for big powers seeking to impose its will on the poor countries".
"[Annan's UN is] a megaphone for big powers seeking to impose its will on the poor countries"
Sudan Foreign Minister Mustafa Usman Ismail
Ismail said possible political pressure on Annan in connection with the oil-for-food scandal had impacted on his stance towards Sudan.
Travel restrictions removed
Also on Saturday, Sudan announced it was cancelling travel restrictions imposed on visiting American diplomats investigating the Darfur issue.
Ismail made the announcement in Cairo and told Suna the decision to lift the restrictions was commensurate with a similar move made by Washington last week.
Sudan began barring American diplomats and members of non-governmental organisations from moving freely in the country a month ago in what it said was a response to Washington's restrictions against Sudanese diplomats in recent years.
In separate news, Sudan sent a delegation to Chad to hold talks with President Idriss Deby, whose government on Friday had accused Khartoum of recruiting, training and arming about 3000 rebels in an effort to destabilise his government.
Sudan announced it was investigating accusations by Chad that Sudan was recruiting and training Chadian rebels.
Chad has accused Sudan of
aiding anti-government rebels
Sudan's ruling National Congress Party said it would investigate the accusations, but said it was a misunderstanding that could be cleared up through official channels.
"We are not going to meet the good deeds of the Chadian government by bad deeds and ingratitude," senior ruling party official Hasan Bargo said, referring to Chadian efforts in the past at mediating in the long peace process in Sudan.