Sudan's army fought rebels in the oil-producing state of South Kordofan last week, both sides said on Saturday.
The rebels said they had killed nine government troops, but the army denied this.
Fighting has taken place since last June in South Kordofan between the Sudanese army and rebels from the northern wing of the Sudan People's Liberation Movement, which wants to topple the Khartoum government.
Clashes spread to neighboring Blue Nile state, which also borders newly independent South Sudan, in September.
The violence has already forced about 417,000 people to flee their homes, more than 80,000 of them to South Sudan, the United Nations estimates.
The SPLM is now the ruling party in the independent south and denies supporting SPLM-North rebels across the border.
The SPLM-North rebels said they had killed nine soldiers, destroyed three tanks and seized military equipment in clashes at Tees near the southern border on Jan 9. They also seized three army vehicles in another attack in the same area on Jan 10, they said in a statement.
SPLM-North is one of a number of rebel movements in underdeveloped border areas who are fighting to overthrow Sudan's President Omar Hassan al-Bashir.
Sudan and South Sudan, who still have to resolve a range of issues including the sharing of oil revenues, regularly trade accusations of supporting insurgencies on each other's territory.
Their armed forces clashed at Jau in a region claimed by both sides last month in a rare direct confrontation.
Refugees fleeing to Ethiopia and South Sudan are reporting food shortages and rising levels of malnutrition.
Questions:
1. How many government troops were killed according to the rebels?
2. What borders the Blue Nile state?
3. How many people have been forced to flee their homes, according to UN estimates?
Answers:
1. 9
2. South Sudan
3. 417,000