The President's convoy was on the way to Bagdogra airport.
The auto involved in the accident was the last vehicle in the President's cavalcade with chief minister Mamata Banerjee's convoy immediately following it.
The vehicle skidded off the road and fell into a gorge at Sonada.
Soon after the rescue mission got over, a tweet on the President's Twitter account said everyone, including the President, are safe.
An officer of the central Intelligence Bureau, a special superintendent of CID, two sub-inspectors of West Bengal police and a state police constable, who was driving the auto, were seriously injured in the accident. Chief Minister Mamata Banerjee herself oversaw the timely rescue operations, due to which all six security personnel travelling in the auto were rescued. His Press Secretary Venu Rajamony said the "the President is safe". The president was on his way to Bagdogra after his three-day trip in North Bengal.
Member Parliament and the President's son Abhijeet Mukherjee also assisted in the rescue operation.
Hailing the prompt rescue work, Banerjee also announced that the state government will "reward those involved in the rescue work". "The police and security men were very prompt in rescuing those who were inside the auto", said Banerjee, whose vehicle was right behind the one that fell off.