The comments by Foreign Minister Mustafa Usman Ismail came on Friday as the United Nations warned of new clashes between rebels and Arab militias in the Darfur region.
Militiamen have increased harassment of non-Arab civilians in western areas, according to villagers there, with four women reporting rapes in the Sisi region.
On Monday, UN Secretary-General Kofi Annan said in a monthly report on Darfur that despite numerous ceasefire agreements, the Sudanese government, its Janjawid militia allies, and rebel groups were increasing military action.
Ismail, speaking to leaders at the two-day Asian-African Summit in the Indonesian capital, Jakarta, denied allegations that the inter-tribal violence in Darfur amounted to genocide, and defended the sending of government security forces to the region.
"The government of Sudan has a duty to respond to both the rebellion and the subsequent breakdown in law and order in parts of Darfur," Ismail said.
"The Sudanese judiciary is, and has always been, willing and capable of assuming its responsibilities"
Mustafa Usman Ismail,
Sudan foreign minister
"There are now joint border patrols by Chadian and Sudanese security forces. These patrols are a major step towards ensuring security and protection of the population in the region."
An estimated 180,000 people have died in the conflict since February 2003, when two non-Arab rebel groups took up arms against the Arab-dominated government to win more political and economic rights for Darfur's African tribes. Sudan is accused of backing Janjawid fighters, who are blamed for raping and killing non-Arab civilians - allegations the government has denied.
The UN Security Council has demanded war-crime suspects be handed over for trial before the International Criminal Court (ICC), a demand Sudan has rejected.
"The Sudanese judiciary is, and has always been, willing and capable of assuming its responsibilities," Ismail said. "The government has brought before the courts persons involved in violations of human rights. Scores of such persons have already been arrested and tried."