Rebel group to disarm in Democratic Republic of Congo Congolese army soldiers march into Kibumba town in eastern Congo Monday, October 28. NEW: More than 8,000 refugees fled to Uganda in recent days, UNHCR says NEW: Congolese government calls M23 announcement "step in right direction" A rebel leader promises his group will end its campaign and disarm Rebels briefly held the city of Goma last year before being driven out (CNN) -- A rebel group that fought the government of the Democratic Republic of Congo for nearly two years announced Tuesday it would disarm. In a statement on the Facebook page for M23, leader Bertrand Bisimwa said the group would immediately end its rebellion and "pursue, by purely political means, a search for solutions to the profound issues that led to its creation." The move came a day after the group and the Congolese government agreed to a ceasefire, during talks in South Africa. Previous talks took place in Uganda. "To this effect, the major general and all unit commanders of the of the Congolese Revolutionary Army are asked to prepare the troops for the disarmament process," Bisimwa's statement added. "This is a hopeful first step toward peace and prosperity in this region," said Russ Feingold, the U.S. special envoy to the Congo and the Great Lakes region. He predicted that the agreements could be signed "in the next few days." But, he told CNN's Christiane Amanpour from Johannesburg, South Africa, "no one should mistake this as the final solution to this problem." He noted that dozens of armed groups fighting over complex issues have killed more than 5 million people in the past two decades in the region. "We need a broader political dialogue to solve that," he said. Feingold urged that amnesty not be granted to those who committed war crimes or crimes against humanity, but said he hoped that the "vast majority" of M23 members would be able to reintegrate into Congolese life. The Congolese government called the move a "step in the right direction" which came after rebel forces were defeated in their last strongholds by Congolese army and security forces. A government spokesman said the rebel group and government officials would eventually sign an 11-point declaration, according to a statement on the website of the state-run Congolese Press Agency. However, the spokesman said, the declaration would only be signed after the government could be certain that M23 members were taking the ceasefire and disarmament plan seriously. The announcement by M23's leader came as a spokesperson for the U.N. High Commissioner for Refugees said in a statement Tuesday that 10,000 people had fled in recent days across DRC's eastern border at Bunagana into southwest Uganda's Kisoro district, a direct result of fighting between M23 and government troops. On Monday, the U.N. group transported 3,624 refugees from the border to the Nyakabande transit center, which is located 23 kilometers away. They represent the largest number in a day since the fighting between the government and M23 began in April 2012, the statement said. Other refugees were walking to the center, where 8,230 people were staying on Tuesday. The center has a capacity of 10,000, it added. "Many of the new arrivals are suffering from dehydration and diarrhea," it said. More than half of the new arrivals were young children, many of whom had been separated from their parents while running from the border, it said. In late October, a U.N. peacekeeper was killed during fighting between Congolese forces and M23 rebels, according to a United Nations statement. The Tanzanian peacekeeper was part the U.N. Organization Stabilization Mission in the eastern part of the vast Central African nation. The mission was joining the Congolese military in an effort to protect civilians about 25 kilometers (15 miles) north of Goma, the largest city in the region, the statement said. Rebels briefly held Goma a year ago. The eastern part of the DRC is a mineral-rich region at the epicenter of a bloody political and ethnic conflict involving its neighbors to the east, Uganda and Rwanda. Clashes in the region over the past year between the M23 rebel group and Congolese government troops have displaced more than 100,000 people, according to the U.N. M23 is named for a March 23, 2009, agreement it accuses the government of having violated. The soldiers, mostly from the Tutsi ethnic group, became part of the national army through that accord. However, they broke away from the Congolese army last year, complaining of lack of pay, poor conditions and failure to receive promised promotions.