* Rebels' political chief to meet Uganda president before summit
* Fighters push towards warlord's home
* U.N. says rebels killed, kidnapped civilians
* Kinshasa protesters allege rape of pregnant women
* Rwanda again denied involvement
By Jonny Hogg and Richard Lough
SAKE/GOMA, Democratic Republic of Congo, Nov 23 (Reuters) - R ebels advanced in eastern Congo on Friday, seeking to strengthen their grip before a regional summit intended to damp down the insurgency in an area long plagued by ethnic and political conflict.
Fighters from the M23 group, who are widely thought to be backed by neighbouring Rwanda, pushed south along Lake Kivu near the new rebel stronghold of Goma on the Rwandan border.
In the capital Kinshasa, protesters accused the rebels of abuses including the rape of pregnant women while the United Nations reported killings of civilians and kidnappings.
The rebels advanced as their political chief Jean-Marie Runiga was due to meet the president of Uganda on the eve of the Kampala summit of leaders from Africa's Great Lakes region.
Regional and international leaders are scrambling to halt the latest violence in the Great Lakes area, fuelled by a mix of local and regional politics, ethnic rifts and competition for big reserves of gold, tin and coltan, an ore of rare metals used in electronics and other high-value products.
Another rebel contingent moved north from the road junction at the town of Sake, scene of a failed counter-offensive by government forces.
A Reuters correspondent in Sake said rebels were in control after Thursday's battle, which had been the first sign of a government fightback since the army abandoned Goma, a frontier city of one million, on Tuesday.
" There was heavy fighting," said pastor Jean Kambale. "It's M23 who control the town. They never lost it."
Fighters for the group - which said after taking Goma that it would march on Kinshasa 1,000 miles (1,600 km) away to defeat Kabila - met no resistance as they probed south from Sake.
Those rebels who pushed north from Sake moved closer to the home town of Bosco Ntaganda, a Rwandan-born warlord who many say controls the insurgency and is wanted for war crimes by the international court at The Hague.,
Thousands of refugees were fleeing the fighting and heading for Goma, where aid agencies have a significant presence, along with U.N. peacekeepers who stood back when the rebels moved in.
U.N. aid agencies painted a bleak picture of the aftermath of the fighting, which they estimate has displaced 140,000 people in and around the lakeside city of Goma.
A rebel spokesman said M23 had "demilitarised" Goma, moving soldiers out and securing it with a makeshift police force.
"Our soldiers are outside the city. We demilitarised two days ago," said M23 spokesman Vianney Kazarama.
A Reuters correspondent saw hundreds of people in Goma's stadium on Thursday registering to become police.
In the distant capital, hundreds of women marched on Friday on the headquarters of the U.N. mission to protest against the rebellion. "I am saddened by everything that is happening over there. Pregnant women are raped and mistreated. I am marching in solidarity with them," said one of the women, herself pregnant, who asked not to be named.
The women, clad in black, carried banners calling for peace and criticising Congo's tiny but militarily powerful neighbour. "No to Rwanda!" read one.
Rape during conflict is well documented in Congo, with rights groups saying it is used as a weapon of war.
In a statement on Friday, U.N. Human Rights chief Navi Pillay's spokesman said they had reports of rebels killing at least nine civilians, wounding dozens more and carrying out a series of kidnappings. Government troops had also committed abuses, including looting, the spokesman said.
The crisis has raised tensions between Congo and Rwanda, which Kinshasa, backed by U.N. experts, accuses of secretly supporting the rebels.
Kigali has a history of meddling in Congo's conflicts but Rwandan President Paul Kagame has repeatedly denied involvement, accusing Congo and world powers of seeking a scapegoat for their failures. "It doesn't matter how many times you repeat lies about us, it doesn't make it the truth ... we will not accept it," the Rwandan presidency said on its official Twitter account.
In Goma, capital of North Kivu province, M23 fighters showed journalists on Friday an arms cache they said the army abandoned when it fled the town. Weapons on display included multiple rocket launchers, artillery canons, hundreds of mortars, anti personnel mines, and stacks of ammunition.
"Kabila is gone, With this, Kabila leaves. We'll take this to the front. If he doesn't negotiate, we continue," said Colonel Seraphin Mirindi, a senior rebel officer.
Previous uprisings in Democratic Republic of Congo, among them one led by Kabila's father, have been launched from the area, where a mix of colonial-era borders, mineral deposits and ethnic rivalries has caused millions of deaths during nearly two decades of turmoil dating from the 1994 genocide in Rwanda.
Red Cross officials had so far retrieved bodies of 31 people killed in fighting for Goma, UNICEF said.
The rebels have had a mixed welcome in areas taken this week, with some welcoming promises of change but many also tired of years of conflict and expecting abuse by gunmen on all sides.
Fearing more fighting, thousands of people, clutching children and belongings, were on the move around the lake on Friday, trudging along the road towards Goma from Sake.
M23 was formed in April by army mutineers who accused Kabila of reneging on a peace deal from an earlier conflict. It now says it plans to "liberate" the whole country and has rejected a call from regional states to withdraw from Goma.
While Kabila's armed forces are on the back foot, analysts remain sceptical the rebels can make good on their threat to march on Kinshasa in the west without significant, overt support from foreign backers.
The rebels have so far ignored international calls to withdraw from occupied areas and say they are doubtful of Kabila's stated readiness to look into their complaints, since they complain of having already waited months for talks.
Ben Shepherd, an associate fellow at UK-based Chatham House think tank, wrote in a paper that Congo and Rwanda were playing a high-stakes game, with Rwanda risking further international condemnation for reportedly backing the rebels and Kabila potentially facing a backlash over his handling of the rebellion.
"Both will be hoping the other blinks first," he said.