Fighters from the M23 rebel group have captured Goma, the main city in resource-rich eastern Democratic Republic of Congo.
The rebels met little resistance from the army or UN peacekeepers.
The leaders of DR Congo and Rwanda, Joseph Kabila and Paul Kagame, flew to Uganda for talks, amid claims that Rwanda was backing the rebels.
France called for the UN Security Council to strengthen the peacekeepers' mandate to intervene in the conflict.
Mr Kabila has urged people to "resist" the rebels.
Protesters burnt UN and ruling party property in the north-eastern city of Kisangani, as they vented their fury over the fall of Goma.
The UN said it had received reports that the rebels had abducted women and children from Goma.
Aid agencies say tens of thousands of people have fled their homes in the last five days as conflict escalated.
This is the first time since the war officially ended in 2003 that rebels have entered Goma, raising fears that a wider conflict could reignite.
Some five million people died in the DR Congo war, which dragged in neighbouring states - including Rwanda, Uganda, Zimbabwe, Namibia and Angola.
Some crowds reportedly shouted "welcome" and "thank you" as M23 leader Sultani Makenga and hundreds of his fighters entered Goma, which has a population of about one million.
A BBC correspondent says a senior rebel commander told him that if the government refused to enter into talks, they would carry on to Bukavu, another major city in eastern DR Congo.
The 19,000-strong UN force in DR Congo, known by the acronym Monusco, did not intervene.
UN spokesman Eduardo del Buey said peacekeepers "cannot substitute" for the national army, adding that the 1,500 UN troops in Goma held their fire because they did not want to risk civilian lives.
French Foreign Minister Laurent Fabius called for Monusco's mandate to be altered to give it more powers, saying it was "absurd" that the UN force could not stop the rebels.
In a television broadcast, Mr Kabila called on people to defend the country. "DR Congo is today confronted with a difficult situation. When a war is imposed, one has an obligation to resist," he said. "I ask that the entire population defend our sovereignty."
Mr Kabila flew late on Monday to Kampala to discuss the conflict with his Ugandan counterpart President Yoweri Museveni, as well as Rwanda's Mr Kagame.
Rwanda has denied persistent accusations by the DR Congo government and UN that it backs the M23 rebels.
Rwandan Foreign Minister Louise Mushikiwabo said the conflict in eastern DR Congo could only be resolved through talks.
"By focusing on the blame game and ignoring the root causes of conflict in the DRC, the international community has missed the opportunity to help the DRC restore peace," she said, in comments posted on the government's website.
Various rebels groups have been active in mineral-rich eastern DR Congo since the end of the war in 2003.
The latest conflict broke out after a mutiny in the army in April, when a group of former rebels formed the M23, also known as the Congolese Revolutionary Army.
About 500,000 people have fled the fighting since then.
The M23 is largely made up of ethnic Tutsis, the same group which dominates the government in Rwanda.