"The funding has not been flowing as we have been expecting," Ban said. "We are now mobilizing all resources possible."
The money is needed to ensure the poorest countries get vaccine supplies and antivirals if the global epidemic continues to spread, he told a news conference.
World Health Organization chief Margaret Chan told the donors that she wants to mobilize a minimum stockpile of vaccines to 49 of the world's least developed countries as a first step. She did not name the countries.
"Many of the developing countries have weak health systems," said Chan. "They actually go into this pandemic what I call empty-handed. They don't have antivirals. They don't have vaccines. They don't have antibiotics."
The swine flu outbreak has been relatively mild so far and most people recover without taking antivirals, but Ban said it should not be taken for granted that the outbreak will continue to be mild.
Health officials are concerned that people in poorer countries and those fighting other health problems like malaria, tuberculosis, malnutrition and pneumonia might be more susceptible to swine flu.
"For the remainder of this year, it is our estimate that we may need ... over $1 billion," Ban said, without elaborating.
But speaking to donor countries later Monday, Ban said he counted on their support for funding.
"Public funding should come first before we ask for any private fundings," he told government officials.
The United Nations in May asked vaccine producers to reserve a portion of their pandemic vaccine production for poor countries, but has yet to make a specific appeal for general donations.
Some companies have agreed to help. GlaxoSmithKline PLC offered to donate 50 million doses of pandemic vaccine to WHO for distribution to developing countries.
"We hope to mobilize some funds to procure commodities, including antibiotics, antivirals and vaccines to countries," Chan said.
Some 429 people have died of swine flu and over 94,000 have been infected, according to the latest totals by the WHO. But experts fear the number of infected people may be much higher than those confirmed.
Last week, Britain's health minister said the country faces a projected 100,000 new swine flu cases a day by the end of August. Britain is the hardest-hit nation in Europe amid the global swine flu epidemic.
Chan warned governments that the pandemic "could have a devastating impact in the developing world" and urged countries to improve their health systems.
At an EU health conference, Sweden's health minister said Monday that countries must prepare for a second wave of infections that could be deadlier than the current outbreak.
There is a risk the virus could change its character and spread rapidly as European children return to school after summer holidays, Maria Larsson said at the meeting in Jonkoping, Sweden.
British health authorities said Monday that a 9-year-old who had "serious underlying health problems" died after contracting swine flu.
Elsewhere Monday, three athletes tested positive for the virus at the World University Games in Serbia, and a Berlin high school was shut down after eight pupils were diagnosed with swine flu.
In Rio de Janeiro, the Brazilian soccer club Cruzeiro requested that the first leg of the Copa Libertadores final against an Argentine team be postponed because of a swine flu outbreak in Argentina.
The swine flu epidemic has killed at least 44 people in Argentina and led to a public health emergency being declared in the capital of Buenos Aires last week.
By Associated Press Writer Eliane Engeler; AP writer Malin Rising in Jonkoping, Sweden, contributed to this report.
By Associated Press Writer Eliane Engeler; AP writer Malin Rising in Jonkoping, Sweden, contributed to this report