Mr Miliband and Mr Kouchner met Rwandan President Paul Kagame in his country's capital Kigali after visiting camps for displaced people around Goma and holding talks with Congolese President Joseph Kabila in his capital, Kinshasa.
The crisis, even if averted in the short term, will return without a new, vigorous and united political effort
Bernard Kouchner and David Miliband French and British foreign ministers
The Congolese government accuses Rwanda of backing the rebels, but both countries' presidents have agreed to attend a regional summit on the situation in the coming weeks.
In a joint statement, the two European foreign ministers said visiting the area had brought home how necessary it was to end the conflict and improve living conditions for those caught in the middle.
"The immediate needs are obvious. We saw them yesterday," they said.
"The humanitarian needs for food, shelter, water and healthcare must be met through universal provision and secure routes for delivery."
The pair also called for the strengthening of the 17,000-strong UN force in DR Congo, and said bilateral peace agreements already in place between regional powers must be honoured.
UK Prime Minister Gordon Brown has said the international community must "not allow Congo to become another Rwanda", where 800,000 people died in a 1994 genocide that is seen as the origin of the current conflict over the border.
Aid corridor 'vital'
Since fierce fighting began across the eastern DR Congo almost two months ago, some 250,000 people have been forced from their homes, and aid agencies have been forced to suspend operations.
As many as 50,000 displaced have reached Goma while many others have vanished. It is unclear how they are managing to survive.
Refugees in the Democratic Republic of Congo await food
The British and French foreign ministers said establishing an aid corridor to Goma was a top priority.
Visiting the Kibati camp for displaced people north of Goma on Saturday, the ministers and their bodyguards had to push through dense crowds of desperate people.
Correspondents say many were struggling to cook meagre emergency rations while others tried to put up flimsy plastic shelters in the rain.
We want to return to our village, but only if there is security
Others were trying to return to their homes, journeying on foot through territory now controlled by Gen Nkunda, whose rebels are camped out near the city.
"We received no food, so we are returning," Paul Bashoboye Bareke told the AFP news agency, surrounded by his wife and their eight children.
Others saw no point in going home.
"We want to return to our village, but only if there is security. I have not eaten for six days," one elderly woman, Rgwasa Nyakaruhije, told Reuters.
Concerns were heightened earlier in the week when the UN refugee agency said camps sheltering 50,000 refugees in Rutshuru, 90km (56 miles) north of Goma, had been forcibly emptied, looted and razed.
The head of mission for the UN's Office for the Co-ordination of Humanitarian Affairs (OCHA) in Goma said the first aid delivery in a week would be dispatched to Rutshuru on Monday after the rebels and the army agreed to open a humanitarian corridor.
The convoy, which will be escorted by UN troops, will group staff and resources from UN agencies and humanitarian NGOs.
"Our priority is to restart the activities at many health centres in the area of Rutshuru and Kiwanja. We're taking health supplies, water, and sanitation," Gloria Fernandez told reporters.
A senior US official has backed the idea of sending EU troops to help the overstretched UN mission, Monuc.
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