(CNN) -- The political leader of a rebel group in the Democratic Republic of Congo flew to Uganda Thursday for talks with that country's president, two days after his group took over a key city in the eastern part of the DRC.
M23 leader Jean-Marie Runiga Lugerero was summoned to Kampala by President Yoweri Museveni, who is hosting a conference of regional leaders Saturday aimed at ending the crisis in the DRC, according to an M23 source close to Lugerero.
Democratic Republic of Congo President Joseph Kabila and President Paul Kagame of Rwanda are also in Kampala for the International Conference for the Great Lakes Region, which is set to start there Saturday.
The M23 rebel movement gained control of Goma earlier this week and then announced that it plans to "liberate" the entire country.
Fierce fighting erupted Thursday in Sake, a city west of Goma that M23 rebels captured Wednesday. Sake is strategic since it is a gateway to Bukavu, the capital of South Kivu.
Residents were seen streaming out of Sake seeking safety as government forces and other militia groups fought to halt the rebel advance.
Those who remained in Goma Thursday had no water, electricity or gas service, and no way out by land or water.
Oxfam, which is monitoring humanitarian conditions in the area, warned Thursday that the fall of Goma to the rebels creates "a very real risk of complete collapse of state authority and the humanitarian crisis reaching new depths."
It estimates 120,000 people are in urgent need of help, with many sleeping in the open or in schools and other buildings without humanitarian aid.
"People are living in chaotic conditions," Tariq Riebl, Oxfam's humanitarian coordinator, said. "There are real fears that cholera and other fatal water-borne diseases could spread, as shortages of power and water in Goma have left thousands of people with no choice but to get water straight from Lake Kivu."
An M23 spokesman said Tuesday that the capture of Goma, the culmination of several days of heavy fighting against government forces, was just the beginning.
"We will push on to Bukavu, then Kisangani, and finally take Kinshasa and overthrow the government," Lt. Col. Vianney Kazarama said to enthusiastic cheers from a crowd of several hundred at Goma's stadium, according to a Congolese reporter there.
Kazarama said that once the rebels overthrow the government, they will call for elections.
Kinshasa, the country's capital, lies nearly 1,000 miles west of Goma, the capital of North Kivu province.
The eastern part of the DRC, which includes Goma, has been embroiled in violence since 1994, when Hutu forces crossed the border from Rwanda fearing reprisals following the genocide in that country.
The M23 group was named for the peace deal of March 23, 2009, which they accuse the government of violating. The soldiers, mostly Tutsis, became part of the national army through that accord. However, they broke away from the Congolese army in April, complaining they weren't being promoted as promised, and because of a lack of pay and poor conditions.
Tens of thousands of Congolese, already displaced by previous rounds of fighting in the volatile region, have fled camps around the edges of Goma, according to UNICEF and the medical charity Doctors Without Borders.