GOMA (AFP) ― Rebels in the Democratic Republic of Congo on Wednesday claimed control of a town outside the captured city of Goma and threatened to continue their push all the way to Kinshasa, as the U.N. accused them of carrying out summary executions.

“We are not going to stop at Goma, we will go as far as Bukavu, Kisangani and Kinshasa,” M23 spokesman Vianney Kazarama told a crowd massed at a stadium in Goma a day after the rebels overran the eastern city with little or no resistance from U.N. or government troops.

Rebels said Wednesday they had also seized the town of Sake, about 20 kilometers northwest of Goma. They vowed to press on southward to Bukavu, the other major city on the border with Rwanda.

Kazarama also demanded that President Joseph Kabila leave power, claiming he was not the legitimate winner of last year’s disputed presidential election.

But at talks in Kampala, Kabila and the leaders of neighboring Rwanda and Uganda insisted that the rebels must immediately pull out of Goma, the main city in the mineral-rich but deeply impoverished east.

U.N. envoy Roger Meece accused the rebels of carrying out “summary executions” of local leaders in their advance.

Meece told the U.N. Security Council that the ethnic Tutsi rebels who launched their uprising in April were trying to set up “a formal administrative or governing structure” in the region.

“We have received numerous reports of targeted summary executions of those who stand in their way, including government and traditional leaders who resist or fail to cooperate with an M23 administrative structure,” he said.

Meece said that since the fall of Goma there had been demonstrations in several cities against the U.N. presence and the government.

The United Nations and other humanitarian groups have reported killings, abductions, looting and extortion of civilians and fears of a humanitarian catastrophe were growing as electricity and water supplies dried up.

Violent demonstrations erupted in several DR Congo towns, including Kisangani where protesters targeted the U.N. base, as well as a church whose pastor was accused of having M23 ties, a resident said.

Six people were also killed in protests in the town of Bunia, a Western aid worker said. The information could not be immediately confirmed.

The U.N. accuses Rwanda of backing the M23 fighters, charges denied by Kigali, which in turn accuses DR Congo of supporting Rwandan rebels based in the eastern DRC. Kinshasa denies the claim.

The M23 has vowed to fight on unless the government in the capital Kinshasa agrees to talks, and as they consolidated their control of Goma, Kazarama called for police and soldiers to join the rebels.

Experts said it was unclear whether the M23 had taken Goma as a stepping stone towards seizing more territory, or simply to gain greater bargaining power with Kabila.

DR Congo Prime Minister Augustin Matata Ponyio said Kinshasa had “lost the battle but not the war”, and insisted the country’s territorial integrity was “non-negotiable.”

The U.N. defended its peacekeepers after Goma fell, with a spokesman saying a battle for the city would have endangered civilians.

It has around 1,500 “quick reaction” peacekeepers in Goma, part of some 6,700 troops in North Kivu province, backing government forces against the rebels.

The U.N. Security Council on Tuesday unanimously backed a resolution calling for sanctions against two M23 leaders and an end to all “outside support” for the rebels.

U.N. Secretary-General Ban Ki-moon issued a new condemnation of “grave” human rights violations by the fighters, although retreating government troops have themselves been accused of looting.

“Reports indicate that the M23 has wounded civilians, is continuing abductions of children and women, is destroying property and is intimidating journalists,” spokesman Eduardo del Buey said.

Rebels in DR Congo -- the M23 among them -- have been blamed for hundreds of deaths since they launched their uprising in April. The M23 mutinied in April after the failure of a 2009 peace deal that integrated them into the regular army.

Tens of thousands of people have fled their homes or camps around Goma, a city of about one million that is sheltering tens of thousands forced from their homes by conflict.

Goma’s clean water supply was cut Wednesday after electric pumps failed in a broader electrical outage caused by the destruction of power lines.

Aid group Oxfam described the situation as “a humanitarian catastrophe on a massive scale.”

Meanwhile, the International Criminal Court in The Hague said that Bosco Ntaganda, a former army general suspected of being M23’s leader, and Sylvestre Mudacumura, the commander of the FDLR, a Hutu militia group, should be arrested urgently.

Both men are wanted on suspicion of war crimes and crimes against humanity in DR Congo.

Two wars that shook the whole of DR Congo in 1996 and 1997, and then again from 1998 to 2002, both began in the Kivu region, with Rwanda and Uganda playing active roles in both.

Since 1998, more than three million people are estimated to have died from combat, disease and hunger, and 1.6 million have been left homeless.

The former Belgian colony remains one of the world’s least developed countries despite a wealth of cobalt, copper, coltan, diamonds and gold.