(CNN) -- Regional leaders meeting in Uganda on Saturday called on a rebel group in the eastern Democratic Republic of the Congo to withdraw from a city seized by its fighters this week and to "stop all war activities."
The M23 group must also "stop talk of overthrowing an elected government," said a statement issued by the regional leaders at the end of the Great Lakes region summit in the Ugandan capital, Kampala.
It states the rebels should withdraw at least 20 kilometers (12 miles) north of Goma and that the U.N. mission for DR Congo, MONUSCO, should monitor the buffer zone.
The statement also calls on the Congolese government to listen to and resolve the grievances of the rebels, who took control of the city of Goma on Tuesday after days of fighting with government forces.
The M23 group was named for a peace deal reached on March 23, 2009, which it accuses the government of violating.
Congolese President Joseph Kabila was among the leaders who attended the conference Saturday aimed at ending the crisis.
Rwandan President Paul Kagame was scheduled to attend, but sent his foreign minister instead, Ugandan officials said. Kagame attended monthly community meetings Saturday where residents plant trees, according to his website.
The Rwandan president met his Congolese counterpart Tuesday in Uganda. After the meeting, the leaders issued a statement calling on the rebels to pull out of Goma.
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 the Congolese president 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 the sharing out of positions in the national army, an equitable distribution of resources and infrastructure development in eastern DR Congo, Abandi said.
"If he (Kabila) does not agree talks now on how we get to implement the 2009 truce, then he will take full responsibility of what will happen later."
On Wednesday, another M23 spokesman told crowds at Goma's stadium that his group would fight on.
"President Kabila brought war planes and big guns, but he was unable to defeat us. That is a clear sign that we are part of God's plan, we were sent by God and this will not end here," Lt. Col. Vianney Kazarama said. "We will push on to Bukavu, then Kisangani, and finally take Kinshasa and overthrow the government."
The United Nations and some donor countries have accused neighboring Rwanda of backing the M23 by providing it with arms, support and soldiers. Kagame has repeatedly denied the allegation.
As the latest conflict flares, aid groups are warning of escalating risks of diseases and abductions facing victims fleeing the violence and uncertainty.
International organizations, including Oxfam, World Vision and the United Nations, have been forced to abandon operations in eastern DR Congo.
Their exit leaves the area susceptible to a humanitarian crisis, including spreading attacks and children at risk of kidnappings by groups such as the Lord's Resistance Army.
"UNHCR is extremely concerned about the situation of displaced people in Democratic Republic of the Congo's North Kivu province, especially children and other vulnerable groups," said Adrian Edwards, a spokesman for the world body's refugee agency.
Edwards said his agency works in 31 displaced camps that host about 108,000 people in North Kivu.
"The fighting has meant that we and our partners have not been able to access most of these areas," he said. "Only Mugunga III just outside Goma can be currently visited."
North and South Kivu face the greatest risk.
The Kivus are considered mineral-rich in a country known for its vast reserves of diamonds, gold and copper.
The area's potential for wealth has been plundered by greedy warlords. Civil wars -- most recently in the 1990s through 2003 -- have left millions dead and displaced entire generations.
On Tuesday, the United Nations moved all but a core team to Rwanda to avoid casualties and urged armed parties to ensure civilians' safety.
"In Goma, there have been reports of 60 assaults on civilians to our partners," Edwards said Friday. "Our partners are telling us eight people have been killed, and houses and shops have been looted."
Killings included six women, including one who was pregnant and an additional infant, according to Rupert Colville, a spokesman for the U.N. High Commissioner for Human Rights.
The fighting between M23 and the Congolese army has left the Kivus vulnerable to other armed groups, raising the possibility of the Lord's Resistance Army abducting children, said Marixie Mercado, a spokeswoman for the U.N. children's agency.
"There are other groups operating in the area, which raises the likelihood of recruitment of children," she said.
And the risks are not limited to violence.
"Before the crisis started, there were already 27,000 cases of cholera reported in the country," she said. " Running water in Goma has just been restored. It had been shut off for over a week and there are huge numbers of children collecting water from Lake Kivu which obviously raises the risk of disease spreading."
The U.N.'s refugee agency estimates that more than 589,000 people have been displaced in North and South Kivu since the beginning of the year. Oxfam estimates that 230,000 are affected by this crisis alone.
CNN's David McKenzie and Zarifmo Aslamshoyeva contributed to this report.