Afterwards, they urged the full implementation of peace agreements between Congo and Rwanda, and the disarming of militias.
The US Assistant Secretary of State for African Affairs, Jendayi Frazer, has meanwhile said that her country is in favour of an EU force being deployed to help the overstretched UN mission, Monuc.
"An outside force... could come to provide humanitarian assistance to protect access to the civilian population so the humanitarian workers could serve them," she said after meeting Rwanda's president.
After holding talks with the Congolese government on Sunday morning, the British and French foreign ministers flew together to Goma, the provincial capital of the volatile east, to see for themselves the scale of the humanitarian crisis.
At the Kibati camp for displaced people, 20km (12 miles) north of the city, Mr Miliband said there was a pressing need for emergency relief to be able to reach the thousands of people who had fled the fighting, and for peacekeeping troops to ensure the safety of aid organisations.
"Humanitarian aid needs security and that is the absolute priority for these people, who need safe and secure routes for the humanitarian aid that has been promised," he told reporters.
Mr Miliband said the UK government did not support sending British troops to reinforce Monuc. The current 17,000-strong force needed to be more effectively deployed in eastern DR Congo, he argued.
"What these people need is quick help," he said. "The first priority is to get them properly deployed, with the right sort of flexibility and the command structures that are delivering for the people here."
Mr Miliband also acknowledged the EU needed to do more to support the humanitarian crisis, but he said there could be no lasting solution without a political agreement that included both the Congolese and Rwandan governments.
The head of Monuc, Alan Doss, said that in the coming days he hoped to be able to find ways to reinforce the UN troops in Goma, but stressed: "We do need help. We are stretched. We are engaged on four fronts."
The origin of the ongoing conflict in eastern DR Congo is the 1994 genocide in Rwanda.
Gen Nkunda says he is fighting to protect his Tutsi community from attack by Rwandan Hutu rebels, some of whom are accused of taking part in the genocide.
The Congolese government has often promised to stop Hutu forces from using its territory, but has not done so. There have also been accusations of collusion between DR Congo's army and Hutu guerrillas.
The Congolese government, for its part, has accused Rwanda of backing Gen Nkunda. Rwanda denies this, but it has twice invaded its much larger neighbour in recent years.
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