In Sierra Leone, five people are being infected with Ebola every hour and demand for treatment beds is far outstripping supply, warns the Save the Children charity.
If the current "terrifying" rate of infection continues, 10 people every hour will be infected with the deadly virus in the West African country by the end of October, the London-based organisation warned.
"The scale of the Ebola epidemic is devastating and growing every day, with five people infected every hour in Sierra Leone last week," Save the Children chief executive Justin Forsyth said in a statement.
"We need a coordinated international response that ensures treatment centres are built and staffed immediately."
The charity issued the appeal as Britain hosted a conference in London to gather support for the fight against Ebola in Sierra Leone, its former colony.
Britain has provided 143 new treatment beds so far and promised almost 600 more in the coming months, but Save the Children said other countries must join the fight.
There were an estimated 765 new cases last week, the charity said, but only 327 beds across the country.
The number of cases was likely to be "massively" under-reported, as "untold numbers of children are dying anonymously at home or in the streets", it said.
"We are facing the frightening prospect of an epidemic which is spreading like wildfire across Sierra Leone, with the number of new cases doubling every three weeks," said the charity's country director in Sierra Leone, Rob MacGillivray.
"Children, more than anyone, are suffering painful, anonymous and undignified deaths at home.
"It's very difficult at this stage to even give accurate figures on the number of children who are dying from Ebola, as monitoring systems cannot keep pace with the outbreak."