Four shells struck Kadugli, the capital of South Kordofan. A witness told the independent Sudan Tribune at least one person was killed and several others were wounded, including an employee at a state-run radio station.
The report added that mortar fire coincided with a peace conference in the state. There were no claims of responsibility for the Monday attack.
The U.S. State Department mid-September advised U.S. citizens to avoid traveling to Sudanese states of Blue Nile and South Kordofan. Border conflict has been a problematic issue for Sudan and South Sudan, which gained independence last year as part of a 2005 peace deal.
The government in Khartoum was criticized for neglecting its obligations to bring peace to the troubled Darfur region.
In a statement issued from its embassy in Washington, the Sudanese government said the U.S. government was too harsh in its assessment of the security situation in Darfur.
"The U.S. is clearly sending a negative signal that will only embolden the rebels, thereby making peace in the region all the more elusive," the statement read.
The U.S. State Department's warning said the threat level in Sudan, particularly in Darfur, "remains critical."