Officials also have confirmed 1,070 other cases of infection.
Health Secretary Jose Cordova says most of the new confirmations came from older cases.
The news came Wednesday as Mexico ended a five-day, government-ordered shutdown designed to contain the virus.
Also, dozens of Mexican nationals who were quarantined at hospitals and hotels in China despite showing no symptoms of swine flu
In the United States, health officials say they have moved quickly to identify the genetic characteristics of the swine flu virus and are in a good position to produce a vaccine if one is needed.
Dr. Anne Schuchat of the Centers for Disease Control and Prevention told a House hearing Wednesday that health officials managed to pinpoint the new virus within two weeks. She said, "We have isolated and identified the virus and discussions are under way so that, should we need to manufacture a vaccine, we can work towards that goal very quickly."
Dr. Dennis Carroll, a special adviser on pandemics with the U.S. Agency for International Development said investments to stave off an avian flu epidemic helped lay the groundwork for the quick response to swine flu.
In Texas, health officials on Tuesday announced, and said she was a 33-year-old school teacher who had recently given birth to a healthy baby.
The woman died early Tuesday and had been hospitalized since April 19, said Leonel Lopez, Cameron County epidemiologist.
Health officials stopped short of saying that swine flu caused the death. State health department spokeswoman Carrie Williams said the woman had "chronic underlying health conditions" but wouldn't give any more details.
Lopez said the flu exacerbated the woman's condition. "The swine flu is very benign by itself," Lopez said. But "by the time she came to see us it was already too late."
Tuesday evening, cars filled the driveway and lined the quiet street in front of Judy Trunnell's home in a quiet, new Harlingen subdivision.
A woman who came to the door with tear-streaked eyes declined to give her name or to comment on the death, saying "we're grieving now."
The only other swine flu death in the U.S. was of a Mexico City boy who also had underlying health problems and had been visiting relatives in Brownsville, near Harlingen. He died last week at a Houston children's hospital.
The teacher was from Harlingen, a city of about 63,000 near the U.S.-Mexico border. The school district where she worked announced it would close its schools for the rest of the week, though officials said anyone who might have contracted the disease from her would have shown symptoms by now.
She was first seen by a physician April 14 and was hospitalized five days later. The woman delivered a healthy baby while hospitalized and stayed in the hospital until her death, said Lopez, who declined to give further details about the baby.
Doctors knew she had a flu when she came in, but did not know what kind, Lopez said. The area is undergoing a Type A influenza epidemic right now, of which the swine flu is one variety, he said. She was confirmed to have swine flu shortly before she died, he said.