Officials have estimated that as much as 80% of the eastern Congolese town has been damaged, with many homes completely destroyed. Although the lava stream has now eased, they warn that the situation remains highly unstable.
Some 300,000 refugees have entered Gisenyi, on the Rwandan side of the border, since Thursday. There is little food or water.
But correspondents say it appears many are reluctant to accept what little help there is from Rwanda, which has given military backing to the Congolese rebels who rule the Goma region for several years, preferring to fend for themselves at home.
Others are keen to retrieve their possessions before everything is carried away by the looters who stayed behind in Goma, while others still have tired of waiting for foreign assistance.
The many thousands who have remained in Gisenyi face a third night without shelter.
Urgent appeal
The BBC's Andrew Harding says the people heading back into Goma are walking across hot lava to return to their homes.
He says the traffic goes both ways - and that some of those who have returned are now heading out again with what possessions that have manage to salvage, or scavenge.
A 50-metre (165-foot) wide stream of molten lava is still rolling slowly through Goma, but several flows from the mountain - which lies 10 kilometres (six miles) away - have now dried up, according to Rwandan volcanologist Dieudonne Wafula.
UN officials estimate that 45 people died after Thursday's unexpected eruption, and concern has also grown over the fate of the inhabitants of at least 14 villages north of the town, which were destroyed
by three rivers of lava flowing from the volcano.
"We are asking the international community to come here and bring aid," said Adolphe Onusumba, the leader of the Rwandan-backed group that controls Goma.
The country has said it is prepared to open 26 emergency camps which would cater for as many as 650,000 people. Two makeshift camps were in operation on Saturday.
One, at Nkamira - about 20 kilometres (12 miles) east of Gisenyi - had only taken in some 1,000 people by late Saturday, aid officials said.
The other is at Mudende, a former university campus used until very recently as a "re-education camp" for former members of Rwandan Hutu rebel groups.
Biscuits
A Rwandan foreign ministry spokeswoman said the government was making every effort, but it could not cope with the gigantic task on its own.
In New York, United Nations Secretary General Kofi Annan said the full assets of the UN would be used to assist both DR Congo and Rwanda. An assessment team is being sent to the area.
The UK Government has already promised £2m ($2.9m) for the relief effort.
The United States has started dispatching 20,000 wool blankets, 20,000 water jugs and 5,000 dust masks, worth a total of $224,000.
The UN's World Food Programme (WFP) said it was setting up distribution points along the route from Gisenyi to Ruhengeri.
WFP co-ordinator David Stevenson told the BBC that his organisation had enough supplies - high calorie biscuits - to feed about 300,000 for a day.
Mr Stevenson said other agencies had supplies as well, but more were needed.
The last major eruption of the 3,414-metre (11,381-foot) Nyiragongo was in January 1977.
The Rwandan Government has also made an urgent appeal to the international community to help it deal with the crisis, appealing for food, water and blankets.
International aid pledged:
Britain: $2.9m
Belgium: $1.1m
Germany: $270,000
United States: $224,000
Belgium, the former colonial power of both the DRC and Rwanda, has pledged 1.25m euros ($1.1m) in emergency aid, while Germany intends to provide 300,000 euros ($270,000).
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