Rebels in the Democratic Republic of Congo have rejected a call by regional leaders to withdraw from the main eastern city of Goma.
An M23 rebel group leader said their fighters would push ahead to seize more territory until President Joseph Kabila agreed to talks.
Mr Kabila and the Rwanda and Ugandan leaders have jointly appealed to the rebels to pull out of Goma.
About 500,000 people have been displaced by the rebellion since April.
On Wednesday, a long-awaited UN report accused neighbouring Rwanda and Uganda of backing M23, saying the rebel chain of command culminates with Rwandan Defence Minister James Kabarebe.
Both Rwanda and Uganda strongly denied the accusations when the report was leaked last month.
After the fall of Goma on Tuesday, Mr Kabila flew to Kampala for two days of crisis talks with Uganda's President Yoweri Museveni and Rwanda's leader Paul Kagame.
The three leaders issued joint statement calling on the rebels to stop their offensive "immediately" and to withdraw from Goma, which has a population of about one million.
The M23's political chief, Bishop Jean-Marie Runiga, told Reuters news agency that Rwanda and Uganda had no authority to order them to give up the city.
"We'll stay in Goma waiting for negotiations," he is quoted as saying.
"They [government forces] are going to attack us and we're going to defend ourselves and keep on advancing."
On Wednesday, Mr Kabila said he would study the demands of the rebels, and would consider negotiating with them.
The M23 was formed in April after a mutiny in the army. The rebels said they were not given army posts promised in a 2009 peace deal.
The M23's gains have raised fears of renewed war in DR Congo, where some five million people died in a conflict from 1997-2003.
The rebels captured the small town of Sake, 27km (17 miles) west of Goma, on Wednesday and threatened to march to the capital, Kinshasa, to overthrow Mr Kabila.
The BBC's Gabriel Gatehouse in Goma says it is unclear whether the rebels' capacity matches their ambitions, but they currently have momentum on their side.
UK Foreign Secretary William Hague and International Development Secretary Justine Greening have said Rwanda and Uganda are threatening regional stability by backing the rebels in resource-rich eastern DR Congo.
Their statement came after the UN security Council discussed a report, drafted by a panel of experts, which accused the two countries of fuelling the rebellion.
"We judge the overall body of evidence of Rwandan involvement with M23 in DR Congo to be credible and compelling. We note that alleged Ugandan involvement is assessed to be of a lower intensity and less systemic than Rwanda's," the statement said.
"We call on both countries to respond in full to the report's findings, and to engage openly and constructively with the UN process."
The UN's DR Congo envoy Roger Meece said the UN had received numerous reports of rebels carrying out "summary executions of those who stand in their way" since they captured Goma.
The rebels entered Goma on Tuesday, skirting round a UN compound as Congolese army forces retreated.
France has heavily criticised the failure of the UN force, which has about 19,000 troops, to stop the rebels.
The UN defended its actions, saying it had fired hundreds of rockets in an effort to block the rebel advance on Goma.
The UN Security Council has adopted a resolution condemning the rebel seizure of Goma and calling for sanctions against M23 leaders.