The World Health Organisation says there have only been seven laboratory-confirmed swine flu deaths, all in Mexico, from 79 confirmed cases around the world.
Mexico has revised its death toll from swine flu from 20 to seven in line with the WHO figures. However, it has raised the toll of "probable" deaths from the influenza A virus, of which swine flu is a variant, to 159 from 152.
The government says more than 1,300 people are in hospitals, some of them in a serious condition, out of a total of about 2,500 suspected cases.
Some bodies have been buried or cremated before they could be tested.
The United States has the highest number of confirmed cases outside Mexico, at 64, while Germany is the latest country to confirm its first case. Cases have also been confirmed in New Zealand, Spain, Britain, Canada and Israel.
Countries with suspected cases include Brazil, Guatemala, Peru, Australia, South Korea, and seven European Union states.
The WHO is convening a meeting of scientific experts on Wednesday to discuss the exact nature of the outbreak. It is urging countries to check their contingency plans for a possible pandemic but also says measures such as travel bans are unlikely to prove effective.
Three countries have suspended flights to and from Mexico in an attempt to stop the spread of swine flu.
Argentina has suspended incoming flights from Mexico for for six days, while Cuba and Canada have suspended flights to and from Mexico for 48 hours.
Canadian airline Air Transat has gone a step further, suspending flights between Canada and Mexico, as well as France, until the start of June.
A cruise company, Carnival Cruise Lines, says it will cancel all stops in Mexico.
Mexico City clamps down
Mexico City has ordered all eateries, bars and other venues to close because of the outbreak. Nationwide school closures have already been ordered by the federal government.
Mayor Marcelo Ebrard said on Tuesday that Mexico was facing a "critical moment" in its battle against the outbreak.
Mexico City officials announced they were also temporarily shutting gyms and sports clubs. Zoos, museums, churches and courts are already closed.
The national football federation said on Tuesday that next weekend's national soccer matches would be played in empty stadiums.