The World Health Organization said it was starting to ship 2.4 million treatments of antiflu drugs to the 72 countries "most in need" on Tuesday.
The agency declined to name the countries, but said they included Mexico, which has been hardest hit by the outbreak with 590 laboratory-confirmed cases and 25 deaths, according to WHO figures.
Other countries included those that have been unable to afford building stockpiles of the drugs.
"Part of the stock will be dispatched today the 5th of May, from Geneva and Basel in Switzerland, Maryland in the U.S. and Dubai in the United Arab Emirates," said WHO spokeswoman Fadela Chaib.
The drugs are from a stock of 5 million treatments of Tamiflu that manufacturer Roche Holding AG donated to WHO in 2005 and 2006, she said.
Roche spokeswoman Martina Rupp in Basel said the company was starting work on the shipments at its Basel headquarters Tuesday.
"It is starting here and it's then distributed to the airports," and shipped on several planes, Rupp told The Associated Press.
Some 1.5 million treatments are stored at Roche's headquarters in Basel, she added. Roche is holding the same number of treatments for WHO in Maryland in the United States, Rupp said.
An additional 2 million treatments are stockpiled elsewhere by WHO, she said.
Each treatment consists of 10 capsules, administered two a day for five days.
She said she didn't know the destination countries because that was up to WHO.
"WHO is telling us where they want us to ship it, and that's what we do. We send it to that particular airport in a country," she added.
WHO on Tuesday raised its tally of confirmed human cases of swine flu to 1,124 from 1,025.
"All the new cases are from Canada," said Chaib.
The number of confirmed deaths remained at 26, she said.
The global body said 21 countries had reported laboratory-confirmed cases.
The United States had reported 286 cases and one death.
Canada had 140 cases, Spain had 54, Britain had 18, Germany had eight, New Zealand had six, France and Israel had four each, Italy and El Salvador had two each, according to the latest figures. Austria, Hong Kong, Costa Rica, Colombia, Denmark, Ireland, Netherlands, Portugal, South Korea and Switzerland had one each.
WHO figures are often behind those reported by national health authorities.