Thousands of refugees are streaming out of Chad into Cameroon, placing heavy strain on the Cameroon town of Kousseri near the border, the UN has said.
It said up to 20,000 people had crossed the river border since Saturday, when rebels stormed the capital N'Djamena.
The UN's refugee agency said aid supplies and better accommodation were urgently needed for the refugees.
The rebels have now retreated from N'Djamena, and France has threatened to step in if they launch another assault.
Former colonial power France has 1,400 troops in Chad and has helped to evacuate foreigners from the city.
On Tuesday, "frightened people were still crossing in a continuous flow" from Chad into neighbouring Cameroon, said the UN's refugee agency in a news release.
Thousands have deluged Kousseri in Cameroon, UNHCR said.
While some have found refuge with relatives, in schools or hotels, it said, between 6,000 and 7,000 were staying out in the open at a transit centre near the bridge.
UNHCR said it planned to move these people to an old campsite some 30km away which could hold up to 100,000 people and was equipped with wells.
Two UNHCR aid airlifts are due to arrive this week in the border area.
More than 3,000 refugees have also gone on to Nigeria.
One refugee, who preferred not to give his name, escaped the fighting in Chad and fled south to Nigeria.
"I am now in Kano but have no money left and don't have my documents," he told the BBC.
"I don't know what to do. I telephoned my friend in N'Djamena and he told me that my mother, my father and my fiancee had all been shot. I don't know whether to cry or kill myself."
France said it would be prepared to intervene in the conflict, after a UN Security Council statement "strongly condemned" the rebel offensive.
Foreign Minister Bernard Kouchner said he "hoped" the French troops in the city would not have to intervene.
President Nicolas Sarkozy said France would "do its duty" if necessary.
The tripartite alliance of rebels, meanwhile, has offered a ceasefire, news agencies reported, but it was unclear on what terms.
Spokesman Abderaman Koulamallah told AFP news agency the rebels were bowing to diplomatic pressure to halt their offensive against the government of President Idriss Deby.
But another spokesman, Henchi Ordjo, told Reuters the ceasefire was conditional on President Deby stepping down.
Prime Minister Nouradine Delwa Kassire Coumakoye was dismissive of the offer.
"Why a ceasefire?" he told French TV station France 24.
"They don't exist any more. With whom would we sign a ceasefire?... We've got them under control."
African Union mediators are due in the city to try to end the fighting.
The violence has led the European Union to delay sending its planned peacekeeping force to Chad. More than half of this 3,700-strong force will be French.
The force was meant to protect refugees displaced by the conflict in Darfur and aid workers.
The latest rebel offensive began on the day the first troops had been meant to arrive.
Chad has accused Sudan of backing the rebels to stop the peacekeepers getting too close to Darfur. Sudan denies the charges.