President Joseph Kabila threw more than 20,000 soldiers into a major campaign on December 3 to snuff out Nkunda's three-year-old rebellion, which draws on some 4,000 disciplined and battle-hardened Tutsi fighters.
The army initially made rapid gains in a two-pronged offensive before meeting dogged resistance in the rugged hills on the threshold of Nkunda's fiefdom, close to the border with Rwanda where the rebel leader enjoys support.
Insurgents attacked government positions east of the village of Rumangabo, around 40 km (25 miles) north of the provincial capital Goma, at around 5.30 a.m. (0330 GMT) on Tuesday.
On Monday, Nkunda loyalists wrested back control of the hilltop villages of Karuba and Bihambwe as well as the heights above the town of Mushake, 35 km west of Goma, which government forces had taken on Wednesday.
Congo's U.N. peacekeeping mission (MONUC) said the army had withdrawn from advanced positions on the road north towards the towns of Kirolirwe and Kichanga, two of Nkunda's strongholds.
In a state of the nation address last week on the first anniversary of taking office, Kabila promised to end Nkunda's uprising at all costs and pacify eastern Congo after a tumultuous decade following the toppling of dictator Mobutu Sese Seko in 1997.
Defence Minister Chikez Diemu reassured Congolese in an address on state television late on Monday that despite some setbacks, the campaign remained on track.
"There was a spill-over at Mushake, but there is no impact on the offensive. There's no reason to panic," he said.
Nkunda first led two brigades of army troops into the bush in 2004, saying he was doing so to protect eastern Congo's Tutsi minority.
Renewed fighting erupted in August when he abandoned a January peace deal and withdrew thousands of his fighters from army brigades, accusing the government of supporting his Hutu tribal foes.
More than 400,000 people have fled fighting between Nkunda's insurgents, government soldiers, Rwandan Hutu rebels and local Mai Mai militia in the past year.