The Democratic Republic of Congo's government has rejected an ultimatum by rebels to start talks, as fighting continues near the city of Goma.
The M23 rebels advanced to within a few kilometres of Goma on Sunday, causing tens of thousands of residents to flee.
On Monday, the rebels demanded that government forces withdraw within 24 hours and open dialogue.
The UN Security Council has condemned the rebel advance - the most serious since July in the resource-rich region.
The streets of Goma were deserted on Monday, except for the rare army or UN vehicle, AFP news agency reports.
The M23 rebels said in a statement that if the government failed to hold "direct political negotiations" within 24 hours, they would "pursue the resistance against the government of Kinshasa until it falls", AFP reports.
DR Congo government spokesman Lambert Mende said the rebels were "fictitious forces" backed by neighbouring Rwanda to "hide its criminal activities" in the east.
"We prefer to negotiate with Rwanda, the real aggressor," he said.
At the weekend, the UN Security Council demanded an end to outside support for the group, noting they were well equipped.
Last month, a UN panel of experts said Rwanda and Uganda were supplying M23, also known as the Congolese Revolutionary Army, with weapons in what is seen as an on-going battle for control of the region, which is rich in minerals.
Rwanda and Uganda strongly denied the allegation.
The UK has urged British citizens to leave Goma and advised against all but essential travel to the whole country.
"Any British nationals in Goma should leave, and any in DRC should check the FCO's updated travel advice," said Foreign Minister William Hague.
Government forces and UN troops still control Goma's airport, but the UN says the humanitarian situation is worsening, with some 60,000 internally displaced people fleeing the fighting.
The UN said more than 10,000 fleeing civilians were seen passing near the airport on Sunday.
The rebels captured the town of Kibumba 30km (19 miles) north of Goma, on Saturday, and have since edged closer towards the North Kivu provincial capital, which lies close to the borders with Rwanda and Uganda.
The UN said its peacekeeping forces, Monusco, fought advancing rebels throughout Sunday, using rockets, cannon rounds and helicopter gunships.
"There is a real threat that the city could fall into the M23's hands," said spokesman Kieran Dwyer.
Last week, the UN and US imposed a travel ban and asset freeze on the group's leader, Sultani Makenga.