Spokesman James Gatduel Gatluak, from the Sudan People's Liberation Army, South Sudan's military, told the independent Sudan Tribune that Sudanese forces attacked SPLA positions in Unity state, leaving four injured.
Gatluak said the attack was in stark contrast to international calls for peace.
Tensions between both sides escalated in early April when South Sudanese forces seized the oil-rich town of Heglig along the ill-defined border separating both countries.
Gatluak said Juba was ready to enter into peace talks with Sudan but said the military would maintain a posture of self-defense.
Sudanese President Omar al-Bashir said last week that the time for negotiations was over. Last weekend he declared a state of emergency in three states along the border with South Sudan.
Sudan's official Sudan News Agency said Khartoum's forces during weekend operations in Heglig arrested four "foreigners," including a military officer from South Sudan. They were flown to Khartoum for an official investigation.
South Sudan gained independence in July as part of a peace agreement reached in 2005. The deal ended one of the bloodiest wars since World War II, though ethnic conflicts, disputes over oil and border skirmishes are threatening the fragile peace.