Rebels have been fighting government troops in eastern DR Congo since August.
DR Congo has accused UN peacekeepers of failing to stop rebels from killing civilians in the east of the country.
Reading out a communique by the seven leaders present at the summit, Kenyan Foreign Minister Moses Wetangula said the peacekeepers' mandate should be amended to give them "peace-making" capabilities and rebel groups in the region should be disarmed according to existing agreements.
The government has denied launching a counter-offensive
"There should be an immediate ceasefire by all the armed men and militias in North-Kivu," he added.
"There should be establishment of a humanitarian corridor throughout the area to ensure immediate address of the humanitarian situation and tragedy."
Earlier, Mr Ban criticised the recent offensive by Gen Laurent Nkunda's CNDP rebels.
"The recent military offensives by the CNDP have radically compounded the situation, led to severe humanitarian consequences and thrust the eastern DRC once more into a phase of heightened crisis. This crisis could engulf the broader sub-region," Mr Ban said, quoted by AFP news agency.
"As leaders of Africa, you have a historic responsibility, it is a critical moment for the Great Lakes region, and for Africa as a whole. We must put the cycle of violence behind us."
Mr Ban on the "violent hostilites" in DR Congo
The BBC's Mark Doyle in Nairobi says Mr Ban's words are diplomatic code telling Rwanda to stop supporting Gen Nkunda.
However, in a separate development a Uruguayan officer serving with the UN peacekeepers in DR Congo said the government side was being reinforced by Angolan troops.
The officer spoke to international news agencies in Goma, saying the Angolans had arrived there four days ago.
Two eye-witnesses have told the BBC they have seen Angolan troops in the area.
Angola is an ally of the Congolese government and has been invited by Mr Kabila to provide military assistance. But its government has said it will not intervene directly.
Angola and Zimbabwe both supported DR Congo with troops during the 1998-2003 war.
Gen Nkunda is not attending the talks, but former Nigerian President and UN special envoy Olesegun Obasanjo said he would be given a copy of the communique and his reaction would determine the international community's next move.
However, AFP quoted a CNDP spokesman as saying that the summit had turned out to be "for nothing".
UN peacekeepers said gunfire erupted on Friday just north of the city of Goma, where rebel forces halted their offensive last week.
You cannot fire when you have civilians on the road running in all directions - if you start firing in that situation you end up killing a lot of civilians
Thousands of refugees in the nearby town of Kibati are said to have fled towards Goma when the mortar and small arms fire broke out.
The UN High Commissioner for Refugees said the fighting had interrupted the distribution of aid in the town.
Meanwhile, the UN said it was investigating reports that rebels led by Gen Nkunda had killed civilians in their homes in the eastern town of Kiwanja on Thursday.
At least 12 bodies were found in the town, which was retaken by rebels loyal to him earlier this week.
Gen Nkunda claimed his fighters, who have also seized control of the town of Nyanzale, about 80km (50 miles) north-west of Goma, had attacked armed pro-government militia.
A spokesman for the UN in DR Congo, Madnodje Mounoubai, told the BBC that the UN was doing its best to help civilians, but that peacekeepers could not fire at rebels when they were surrounded by civilians.
"You cannot fire when you have civilians on the road running in all directions. If you start firing in that situation you end up killing a lot of civilians," he said.
The situation in DR Congo has been described as a humanitarian catastrophe, and an estimated 250,000 people have been made homeless by the conflict.
The UN has 17,000 peacekeepers in DR Congo, making Monuc its largest mission in the world.
But only a few hundred peacekeepers are in the areas affected by the latest violence, and human rights groups have also criticised the UN for failing to prevent the killings.
Gen Nkunda says he is fighting to protect his Tutsi community from attack by Rwandan Hutu rebels, who fled to Congo after the 1994 genocide.
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