A 23-month-old Mexican child has died of swine flu in Texas - the first death from the virus outside Mexico, where it may have killed as many as 159 people.
The child - one of 91 cases of swine flu in the US - had been visiting relatives in Texas when he fell ill.
The World Health Organization said the virus was still spreading, even though it was now from person to person.
And Spain says it has confirmed the first case of swine flu in a person who has not travelled to Mexico.
CONFIRMED CASES
Mexico: 159 suspected deaths - seven confirmed cases
US: one death, at least 91 confirmed cases
Canada: 13 confirmed cases
UK: 5 confirmed cases
Spain: 10 confirmed cases
Germany, New Zealand: 3 confirmed cases each
Israel: 2 confirmed cases
Austria: 1 case
Mapping the outbreak
In pictures: Concerns grow
Mexico: First swine flu cases
The Mexican boy had arrived in the Texan border city of Brownsville on 4 April and developed flu symptoms four days later, the Texas Department of State Health Services said.
He was later transferred to a hospital in Houston, where he died on Monday night.
The cause of death was confirmed on Wednesday by Dr Richard Besser, acting director of the Centers for Disease Control and Prevention.
"Unfortunately this morning I do have to confirm that we have the first death of a child from H1N1 flu virus," he told US TV channel CBS.
Speaking in Washington, President Obama offered his condolences and said the federal government was doing the utmost to contain the virus.
SYMPTOMS - WHAT TO DO
Swine flu symptoms are similar to those produced by ordinary seasonal flu - fever, cough, sore throat, body aches, chills and fatigue
If you have flu symptoms and recently visited affected areas of Mexico, you should seek medical advice
If you suspect you are infected, you should stay at home and take advice by telephone initially, in order to minimise the risk of infection
Q&A: What is swine flu?
Swine flu: How serious a threat?
Can masks help spread?
The quest for a swine flu vaccine
He also urged local public-health bodies to be vigilant and said schools with confirmed cases "should consider closing".
Texas Governor Rick Perry said closing the US border with Mexico was an option, but added that taking that step now would be "a little premature".
The assistant director general of the World Health Organization (WHO), Keiji Fukuda, said that although the virus originated in pigs, it was now being transmitted from human to human.
"It is clear that the virus is spreading and we don't see evidence of it slowing down," he told reporters from WHO headquarters in Geneva.
He added that moving the pandemic alert to five - the second highest - from the current four would be a significant step, but was not necessary at the moment.
He said the WHO would do so if infected people in at least two countries were spreading the disease to other people in a sustained way.
BBC correspondent Matthew Price
From Matthew Price in Oaxaca, Mexico
The first fatal case of the virus is believed to have been contracted here in Oaxaca. It is a tourist centre and the obvious concern is that when the visitors leave, they may take the virus with them.
At the local cemetery, a group of gravediggers pointed me towards a freshly dug plot. The flowers on top had wilted under the sun but still had some colour. Here was the grave of the first confirmed victim of the virus, Adela Gutierrez, 39.
One of the gravediggers, Sergio Castro Lopez, told me people here are worried. They are waiting for the authorities to tell them what they should do.
Earlier the WHO urged caution, saying measures like travel bans were unlikely to prove effective.
France will ask the European Union on Thursday to suspend all flights going to Mexico because of the flu outbreak, Health Minister Roselyne Bachelot said.
In Mexico, the search for the source of the outbreak continues, with the focus on the vicinity of a pig farm in the eastern part of the country.
The Mexican government is urging against jumping to conclusions and is suggesting the possibility remains that the virus originated outside the country.
Schools across Mexico have closed, public gatherings are restricted and archaeological sites have been placed off-limits.
Mexico City's chamber of commerce estimated restrictions in the city were costing businesses there at least 777 million pesos ($57m or ÂĢ39m) a day
http://news.bbc.co.uk/1/hi/world/americas/8024611.stm
The child - one of 91 cases of swine flu in the US - had been visiting relatives in Texas when he fell ill.
The World Health Organization said the virus was still spreading, even though it was now from person to person.
And Spain says it has confirmed the first case of swine flu in a person who has not travelled to Mexico.
CONFIRMED CASES
Mexico: 159 suspected deaths - seven confirmed cases
US: one death, at least 91 confirmed cases
Canada: 13 confirmed cases
UK: 5 confirmed cases
Spain: 10 confirmed cases
Germany, New Zealand: 3 confirmed cases each
Israel: 2 confirmed cases
Austria: 1 case
Mapping the outbreak
In pictures: Concerns grow
Mexico: First swine flu cases
The Mexican boy had arrived in the Texan border city of Brownsville on 4 April and developed flu symptoms four days later, the Texas Department of State Health Services said.
He was later transferred to a hospital in Houston, where he died on Monday night.
The cause of death was confirmed on Wednesday by Dr Richard Besser, acting director of the Centers for Disease Control and Prevention.
"Unfortunately this morning I do have to confirm that we have the first death of a child from H1N1 flu virus," he told US TV channel CBS.
Speaking in Washington, President Obama offered his condolences and said the federal government was doing the utmost to contain the virus.
SYMPTOMS - WHAT TO DO
Swine flu symptoms are similar to those produced by ordinary seasonal flu - fever, cough, sore throat, body aches, chills and fatigue
If you have flu symptoms and recently visited affected areas of Mexico, you should seek medical advice
If you suspect you are infected, you should stay at home and take advice by telephone initially, in order to minimise the risk of infection
Q&A: What is swine flu?
Swine flu: How serious a threat?
Can masks help spread?
The quest for a swine flu vaccine
He also urged local public-health bodies to be vigilant and said schools with confirmed cases "should consider closing".
Texas Governor Rick Perry said closing the US border with Mexico was an option, but added that taking that step now would be "a little premature".
The assistant director general of the World Health Organization (WHO), Keiji Fukuda, said that although the virus originated in pigs, it was now being transmitted from human to human.
"It is clear that the virus is spreading and we don't see evidence of it slowing down," he told reporters from WHO headquarters in Geneva.
He added that moving the pandemic alert to five - the second highest - from the current four would be a significant step, but was not necessary at the moment.
He said the WHO would do so if infected people in at least two countries were spreading the disease to other people in a sustained way.
BBC correspondent Matthew Price
From Matthew Price in Oaxaca, Mexico
The first fatal case of the virus is believed to have been contracted here in Oaxaca. It is a tourist centre and the obvious concern is that when the visitors leave, they may take the virus with them.
At the local cemetery, a group of gravediggers pointed me towards a freshly dug plot. The flowers on top had wilted under the sun but still had some colour. Here was the grave of the first confirmed victim of the virus, Adela Gutierrez, 39.
One of the gravediggers, Sergio Castro Lopez, told me people here are worried. They are waiting for the authorities to tell them what they should do.
Earlier the WHO urged caution, saying measures like travel bans were unlikely to prove effective.
France will ask the European Union on Thursday to suspend all flights going to Mexico because of the flu outbreak, Health Minister Roselyne Bachelot said.
In Mexico, the search for the source of the outbreak continues, with the focus on the vicinity of a pig farm in the eastern part of the country.
The Mexican government is urging against jumping to conclusions and is suggesting the possibility remains that the virus originated outside the country.
Schools across Mexico have closed, public gatherings are restricted and archaeological sites have been placed off-limits.
Mexico City's chamber of commerce estimated restrictions in the city were costing businesses there at least 777 million pesos ($57m or ÂĢ39m) a day
http://news.bbc.co.uk/1/hi/world/americas/8024611.stm