"We have found resistance to Tamiflu on the border. We have observed some cases, few to be sure, in El Paso and close to McAllen, Texas," said Maria Teresa Cerqueira, head of the Pan-American Health Organization office in La Jolla, California.
Cases of A(H1N1) that were resistant to the anti-viral medicine have now been found in the United States, Canada, Denmark, Hong Kong and Japan.
Experts had gathered in La Jolla on Monday to discuss the response to the outbreak, and warned that resistant strains were likely emerging because of overuse of antivirals like Tamiflu.
"In the United States Tamiflu is sold with a prescription, but in Mexico and Canada it is sold freely and taken at the first sneeze. Then, when it is really needed, it doesn't work," said Cerqueira.
The Tamiflu-resistant cases were reported as South Africa and India both announced their first fatalities from the A(H1N1) virus, which emerged in Mexico in April and has since spread worldwide, gaining pandemic status.
In South Africa, health authorities said Ruan Muller, a 22-year-old student at Stellenbosch University near Cape Town, had died after contracting the virus.
"He died on the 28th (of July), but there had to be some testing done to ensure the cause of death. It was the A(H1N1) influenza," said Fidel Hadebe, spokesman for South Africa's Department of Health.
With the world's highest number of HIV/AIDS-affected people, nearly 19 percent of a 49-million-person population, South Africa is considered particularly at risk because people with compromised immunity are more likely to fall prey to the disease.
South Africa's swine flu caseload has increased fourfold since the country's first case was reported on June 14. The government has said its stockpile of Tamiflu will only be used for the seriously ill, but that schools may also be closed on a case-by-case basis.
In India, authorities said a 14-year-old girl in the western city of Pune became the country's first fatality from the virus.
The teenager first felt unwell on July 21, complaining of a sore throat, runny nose and headaches. She returned to school the following day after the general symptoms improved, the Ministry of Health and Family Welfare said.
She then developed a fever again on July 25 and two days later was admitted to a private clinic for treatment. She was put on a ventilator in an intensive care unit and was treated with Oseltamivir, a generic brand of Tamiflu.
"Her condition deteriorated again with multi-system involvement and (she) expired on the evening of 03.08.09," the ministry said in a statement.
Meanwhile, the Russian state health agency warned the country's football fans to stay away from the national team's World Cup qualifying tie with Wales in Cardiff on September 9.
"This would be an extremely unnecessary and inappropriate undertaking at a time of a flu epidemic," the head of Russia's state health agency Gennady Onishchenko said, according to local news agencies.
Onishchenko expressed fear that "the expressions of emotion on the part of football fans involving intense shouting" could lead to the airborne transmission of the flu virus.
Russia has to-date been relatively spared by the swine flu pandemic, with just 55 confirmed cases in the country.
Experts remain puzzled as to why different countries have not always been affected to the same degree, with England and Scotland both heavily hit proportionately, yet neighboring France's tally appearing light by comparison.
Some have argued that gargantuan sums being spent by rich economies on a disease that is no more lethal than seasonal flu are grotesquely disproportionate when thousands die each day of diseases which receive less media coverage.