The TAM airlines Airbus A320 is thought to have slid off the end of the runway as it landed in very wet conditions. Concerns had been raised about the safety of the runway during heavy rain. There had been persistent, heavy rain in the two hours preceding the accident.
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The BBC's Gary Duffy in Sao Paolo says the weather has been bad for much of the day and there has been concern for some time about safety at Congonhas during heavy rain. In February, a judge briefly banned flights in and out of the airport, which is the busiest in Brazil.
Pilots had complained that water was pooling on the surface of the landing strip, making braking difficult and occasionally causing planes to skid out of control. Remedial work, including laying a new surface, has been carried out in recent months.
However, a much smaller plane skidded off the runway before stopping on grass in similar weather conditions on Monday. No-one was injured in the incident.
Air safety in Brazil has been a major issue since a crash last year when a passenger plane collided with an executive jet over the Amazon, our correspondent says. Some 154 people died in that incident, which was, at the time, the worst air crash in the country's history.