The Congolese army claims to have killed 120 rebels in eastern Congo.
Twelve Congolese troops were also killed in the fighting, according to a government spokesman.
Fighting between Congo's army and M23 rebels began on Sunday afternoon following the arrival from Rwanda of more than 100 armed men disguised in women's clothing, residents said.
A report by a United Nations panel of experts studying Congo claims that Rwandan soldiers have joined the M23 in recent months, a claim that Rwanda denies.
Peace talks between the Congolese government and the M23 stalled again last week as the head of the M23 delegation, Rene Abandi, complained that the head of the government delegation had left the talks.
The United Nations mission in Congo said the fighting broke out after M23 had been reinforced and had attacked government forces. The UN mission said it is ready to use lethal force to protect civilians and "any attempt by the M23 to advance towards Goma will be considered a direct threat to civilians".
There were no reports of UN peacekeepers taking part in the fighting.
There has also been renewed fighting further north on Congo's border with Uganda, where an Islamist Ugandan rebel group has occupied several villages near the town of Beni. More than 60,000 civilians have fled from the area to Uganda, according to the UN refugee agency.