Yesterday, the humanitarian organisations were still engaged in frustrating talks in Kinshasa with the Zairean government about the delivery of supplies to the most needy areas. Large numbers of desperate refugees are understood to be gathered around the town of Lobutu, to the east of Kisangani, which is set to become the centre for the growing relief operation.
"The Zairean government is making things difficult for the aid agencies because they are afraid they'll freeze the refugee problem for good," one Western diplomat in Kinshasa said. "The Zaireans want the refugees to go back to Rwanda, not to settle even deeper inside Zairean territory."
But there is another problem. Almost one month after eastern Zaire's refugees started fleeing their camps - and one week after the first reports that they were dying of disease, hunger and thirst - there is still no certainty as to where most of them are.
More than 1 million Rwandan and Burundian refugees, as well as countless thousands of displaced Zaireans, have been driven deep into the inhospitable interior of Zaire by fighting raging in the east of the country. In the forests and among the hills of one of Africa's remotest regions, they are still beyond the reach of the international aid agencies.
"We hope to have a better idea of their location by the end of the week", Sergio Vieira de Mello, of the United Nations High Commissioner for Refugees (UNHCR), said.
"A large concentration from one camp has been spotted from the air but we don't know where most of them are. We can't say for certain if they are dying in large numbers but we know their food probably ran out at the end of last week."
Having escaped the fighting between the Zairean army and the rebels who have taken control of much of the east, the fleeing mass of humanity is now prey to the degradations of bureaucracy.
Aid convoys which crossed from Rwanda into eastern Zaire were yesterday stalled as negotiations continued between aid officials and the rebel leader, Laurent Kabila.
The rebels were insisting that their authority in the region be recognised by the United Nations before the distribution of food and blankets could begin.
"The number of refugees who have emerged around Goma saying they are prepared to be repatriated to Rwanda can be counted in hundreds," Mr de Mello said.
"There are also some needy civilians in the town; the situation in Bukavu is much more serious: there's no food or medical supplies and there are lots of wounded."
The cross-border relief effort is for the moment largely symbolic. The far greater need is beyond Goma and Bukavu, which are deep in the heart of Zaire.
But the Zairean government is insisting that supplies must be shipped through the capital, Kinshasa, in the far west of the country.
Although they have lost control of their eastern border region, the Zairean authorities are insisting that aid organisations must not contravene their sovereignty by dealing with the insurgents.
"It's all a bit of a mess," one aid official in Kinshasa said. "The aid operation in the east, with the UN talking to the rebels, has put the Zairean government in a difficult position. I don't think the government is going to be so stupid as to punish the aid organisations but they're unlikely to give immediate approval for a full scale aid effort. They'll probably just approve a bit at a time."
Most of Zaire's missing refugees are Rwandans, members of the country's Hutu majority, who fled their country after at least half a million Tutsis were massacred by Hutu militias in 1994.
They crossed the border to escape advancing Tutsi rebels who put an end to the genocide and formed a new government in Rwanda.
The refugees were again put to flight last month as fighting flared between the Zairean army and Tutsi guerrillas in eastern Zaire.
A UNHCR and United Nations World Food Programme mission is due to arrive in Kisangani today to assess the security situation and humanitarian needs.
So far, no refugees are understood to have reached Kisangani, which has been badly looted by retreating Zairean troops. The International Committee of the Red Cross has been given clearance to deliver a small shipment of supplies to Kisangani today, but not yet to deliver aid to the displaced people beyond the town.