UN ambassadors for France and Gabon, ending a three-day visit to the area, have stressed a political solution to end the fighting, which according to UN figures has displaced over 800,000 people.
But the DRC government wants the international community to impose sanctions against Rwanda and rules out negotiations with the M23.
International envoys as well as the DRC say they want to give a chance to peace efforts for ending the insurgency by M23 rebels in North Kivu province.
Kinshasa and several Western governments say the rebels are backed by Rwanda, a claim angrily denied by Kigali.
Relations between the two neighbors have long been tense. The M23, associated with the Tutsi ethnic group, says it is fighting in part to protect Tutsis from rival Hutu extremist groups.
M23 also claims the DRC government has reneged on a pledge to incorporate the fighters into the national army.
"Let's be serious! The M23 is a terrorist movement," DRC Foreign Minister Christophe Lutundula said late Monday.
Mamy Asumini Kayumba, a resident of Goma, a city of more than one million people increasingly threatened by the advance of M23 fighters, said talking was no solution.
The M23 had previously captured Goma in 2012 before being driven out by a joint Congolese-UN offensive.
"For 30 years we've been living with these atrocities, it's time for it to end," Kayumba said.
For Placide Nzilamba, a civil society activist in Goma, the UN Security Council "should instead go tell the Rwandan government to withdraw its soldiers, who are killing Congolese and shelling cities."
- 'Difficult position' -
But facing insurgents who are gaining ground and see no advantage in accepting a truce, "DRC is in a difficult military position", said Reagan Miviri, a researcher at the Ebuteli think tank in Kinshasa.
And as for negotiations, "it's very hard to offer anything at all to M23 in an election year," given that President Felix Tshisekedi is expected to stand for re-election in December, Miviri said.
Officials appear to have ruled out accepting M23 fighters into the army, and giving them government jobs "would be unpopular," he added.
In one more sign of the hardship facing civilians, Doctors without Borders (MSF) appealed for better aid coordination to help people in remote areas.
Caroline Seguin, MSF's emergency coordinator for North Kivu, said assistance was overwhelmingly concentrated in Goma, whereas more than 150,000 displaced people in Lubero territory north of the city were in a state of "absolute hardship" and had been left to fend for themselves.
Adding to tensions was the weekend decision by Angola, which helped broker the latest cease-fire that collapsed last week, to send a military unit to North Kivu.
The announcement revived memories of the Second Congo War of 1998-2002 that involved nine African countries and nearly tore sub-Saharan Africa's biggest nation apart.
The East African Community has already deployed a regional force consisting of Kenyan and Burundi troops to supervise a theoretical retreat of M23 fighters.
Kinshasa wants the force to have an "offensive" mandate to push back M23 fighters.
But already local resentment against the force is growing, similar to the frustration seen against a UN force that has been unable to stop the fighting despite being in the country for the past 23 years.
Lutundula, the DRC foreign minister, said the Angolan soldiers were not there "to carry out attacks but to see how things are on the ground".
"There is no ambiguity, Angola is within its terms of reference," he said.