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 . Read more : Rebel leader in Uganda for Congo crisis talks . 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 . Read more : Rebels threaten wider Democratic Republic of Congo conflict . `` 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 were n'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 do n'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 . Read more : Can we end rape as tool of war ? 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 .
Uganda : Regional leaders call for the rebels to halt their campaign . M23 wants to topple the government , which is supported by the United Nations . Uganda holds a regional summit Saturday to address the crisis . Oxfam warns of ` ` the humanitarian crisis reaching new heights ''