GENEVA — The Ebola virus outbreak in West Africa risks ballooning into a humanitarian catastrophe without a major surge in international efforts to contain it, senior United Nations officials said Tuesday, estimating the cost of this effort at $1 billion.

The number of people affected by the disease is still rising at an “almost exponential” rate, Bruce Aylward, an assistant director general of the World Health Organization, said at a news conference in Geneva. He said the number of reported cases had climbed to 4,985, including 2,461 deaths. Half of the infections and deaths occurred in the past 21 days, he said, underscoring the acceleration of the outbreak. “We don’t really know where the numbers are going with this,” Mr. Aylward said.

A road map he announced nearly three weeks ago to guide the international response had called for the capacity to manage 20,000 cases, but “that does not seem like a lot today,” he said.

“The numbers can be kept in the tens of thousands,” he said, “but that is going to require a much faster escalation of the response if we are to beat the escalation of the virus.”