M23 rebel soldiers stand guard at the former Congolese army headquarters in Goma, on Friday, after it was abandoned.

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NEW: The United Nations calls on rebels to stop fighting

M23 rebels occupying the city of Goma, Democratic Republic of Congo, refuse to leave

African leaders gave the rebel group until midnight Tuesday to withdraw

The rebels want to talk with Congolese president about breaches of a 2009 peace treaty

CNN  — 

Tension loomed in the Democratic Republic of the Congo city of Goma on Monday night as rebel commanders refused to leave the city ahead of a midnight deadline imposed by regional leaders and the African Union.

African leaders convened in neighboring Uganda over the weekend and released a statement demanding that the M23 group withdraw at least 20 kilometers (12 miles) north of Goma as a condition of initiating negotiations. The leaders called on the rebels to “stop all war activities,” and “stop talk of overthrowing an elected government.”

But M23 leaders said Monday that they will leave the conflict-scarred city only if talks are successful. Both rebel and government troops were massing west of Goma, potentially leading to further clashes as the deadline passed.

At the United Nations, a spokesman for Secretary-General Ban Ki-moon urged the rebels “to immediately lay down their arms in accordance with the agreements reached in Kampala and comply with the immediate withdrawal of their forces from Goma.” The spokesman, Eduardo del Buey, said Ban urged the parties to continue talks “to address the fundamental causes of the conflict.”

He said Ban will also make sure that the U.N. peacekeeping mission MONUSCO is able “to respond to he evolving challenges.” But he added, “The mandate of MONUSCO is to protect civilians. It is not to fight the M23 on its own. That is he responsibility of the Congolese armed forces, and the maintaining of security is the primary responsibility of the Congolese police.”

The M23 group was named for a peace deal reached on March 23, 2009, which it accuses the government of violating. Rene Abandi, a spokesman for the M23 group, told reporters on the sidelines of the conference Saturday that the rebels’ main aim was to force Congolese President Joseph Kabila to agree to talks.

“We want talks over human rights and insecurity (involving) issues contained in the 2009 truce, which he, Kabila, has refused to implement,” Abandi said.

The outstanding issues include positions in the national army, an equitable distribution of resources and infrastructure development in eastern Congo, Abandi said.

Kabila was one of the African leaders who devised a new game plan at the Great Lakes region summit in Kampala over the weekend. But the consortium didn’t just call for concessions from the rebels: The group’s statement also called on the Congolese government to listen to and resolve the grievances of the rebels, who took control of Goma on Tuesday after days of fighting with government forces.

In Goma itself, citizens are getting frustrated with M23, because many shops and all banks haven’t opened, and only a few students have trickled back to school.

International organizations such as Oxfam and World Vision and the United Nations have been forced to abandon operations in eastern Congo. Now, aid groups are warning of escalating risks of disease and abductions facing victims fleeing the violence and uncertainty.

CNN’s David McKenzie and Joseph Netto contributed to this report