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The death toll is expected to rise quickly as rescue teams flood into the worst-affected towns - Bhuj, in the state of Gujarat, and the nearby city of Ahmedabad.
Indian Prime Minister Atal Behari Vajpayee said the country was meeting the emergency on a "war footing", and urged everyone to "rally round and fight the calamity".
Indian officials say more than 2,000 bodies have been recovered so far. Thousands more are still thought to be trapped inside collapsed buildings, including some 400 children inside a school building in Bhuj, near the epicentre.
Floodlights were set up as night fell to help rescuers using crowbars and their bare hands to search through the rubble. Volunteers, friends and neighbours joined them to dig with whatever tools they could find.
A Red Cross official told BBC News Online that Bhuj contained many old buildings susceptible to earthquake damage.
The Home Minister of Gujarat, Haren Pandya, said people had been told to evacuate old buildings and those which have developed cracks.
Local authorities said that government buildings were constructed to withstand earthquakes but most private buildings were not.
The quake struck at about 0850 local time (0320 GMT). It was a public holiday, and many people were out on Republic Day parades or still at home.
Medical facilities are in crisis, with many hospitals damaged by the quake and others overwhelmed by the demand for treatment.
Thousands of people camped outside the air force hospital in Bhuj waiting for treatment. At another hospital in the city, doctors were forced to treat patients on the street.
Anil Chadha, superintendent of Ahmedabad's Civil Hospital, said: "This was probably one of the worst experiences I have ever had - you could call it the longest day."
A rescue operation involving Indian army troops is under way.
The quake was measured at a magnitude of between 6.9 and 7.9, and was felt as far away as Bangladesh, Nepal and the town of Pondicherry in south-east India where people fled in panic from a Republic Day parade.
In neighbouring Pakistan, at least eight people died, including two children in the city of Hyderabad who were killed when their home collapsed.
The death toll in the Gujarat earthquake eventually rose to 25,000. A million people were left homeless.
In the aftermath there was angry criticism from those in urban areas that the authorities failed them. Most aid agencies had concentrated on damaged rural villages where it was easier to reconstruct houses.
The Chief Minister of Gujarat, Keshubhai Patel, resigned in October after angry protests at the slow pace of relief and rehabilitation.
A year later many were still living in tents and shelters in primitive conditions with little sign of damaged houses being redeveloped.
Millions of pounds in emergency aid were raised all over the world to help rebuild communities with the help of international agencies.
But in 2002 the Disasters Emergency Committee published a report which was critical of UK aid agencies in the aftermath of the earthquake in Gujarat.
The report said the agencies could have worked better with local groups, and said they underestimated the scale and effectiveness of the Indian government response.
Pakistan suffered another terrible earthquake in October 2005 in which more than 20,000 died.
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