Sake, Democratic Republic of Congo (CNN) -- Anti-government rebels on Friday continued their march through the eastern part of the Democratic Republic of Congo, withstanding an army counterattack to maintain control of the strategically important town of Sake.
The town is on the road to Bukavu, the capital of South Kivu, and a group of fighters started to march in its direction, journalist Phil Moore told CNN.
Moore and U.N. spokesman Kieran Dwyer said the M23 fighters held Sake after two days of battling government troops in the town they first entered Wednesday.
The United Nations, which supports the Congolese army, as well as Britain have condemned the rebel campaign intended to overthrow the government.
On Friday, the Congolese army was near the town of Minova, about 15 miles south of Sake, according to Moore.
Residents fled ahead of M23's progress, Moore said, and a second group of M23 fighters was heading north to the town of Masisi.
The fighting continued despite a joint statement Wednesday from the leaders of Congo, Uganda and Rwanda that called for M23 to halt its rebellion and enter talks with the Kinshasa government.
"The M23 rebel group must immediately stop its offensive and pull out of Goma," the statement said, adding that the Congo government committed itself to addressing rebel complaints.
The latest unrest continues a cycle of violence and misery in Eastern Congo, a mineral-rich region at the epicenter of political and ethnic conflict involving its neighbors to the east, Uganda and Rwanda.
The area has been embroiled in violence since 1994, when Hutu forces crossed the border from Rwanda fearing reprisals after the genocide in that country.
The M23 group was named for a peace deal of March 23, 2009, which it accuses 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.
The political leader of M23, Jean-Marie Runiga Lugerero, flew Thursday to the Ugandan capital of Kampala for talks with President Yoweri Museveni, who is hosting a conference of regional leaders Saturday aimed at ending the crisis in Congo.
Dwyer said the Kampala summit, which also will include Congo President Joseph Kabila and Rwandan President Paul Kagame, would be scrutinized for any political impetus to stop the violence on the ground.
"There does need to be political solutions to this," he said. "I don't think battlefield solutions are going to be the answer in and of themselves."
The United Nations and some donor countries have accused neighboring Rwanda of backing the M23 by providing it with arms, support and even soldiers. Kagame has repeatedly denied the allegation.
On Tuesday, the rebels gained control of Goma, the capital of North Kivu province, though U.N. forces continued to control the airport.
At a rally at Goma's stadium, an M23 officer declared the group's military goals.
"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, according to a Congolese reporter there.
Mark Simmonds, the UK minister for Africa, arrived in Kigali, Rwanda, on Thursday and immediately issued a statement saying "there can be no attempt to unseat the legitimate government of the Democratic Republic of Congo." He called on the Congolese government to "address the underlying causes of the conflict."
"I call on the M23 to stop its advance and to withdraw from Goma immediately," Simmonds said.
Oxfam, which is monitoring humanitarian conditions in the area, warned Thursday that the fall of Goma to the rebels poses "a very real risk of complete collapse of state authority and the humanitarian crisis reaching new depths."
It estimated that 120,000 people were in urgent need of help, with many sleeping in the open or in schools and other buildings without humanitarian aid.
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.
CNN's Tom Cohen, David McKenzie and Joseph Netto contributed to this report