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Authorities in Delhi say their action was intended to prevent a direct attack by Pakistani forces against India.
On 25 August, Pakistani soldiers launched a covert operation across the ceasefire line, established in 1949 after the first Indo-Pakistani war, into Indian-administered Jammu and Kashmir.
Since then there have been a number of clashes along the ceasefire line, but this is the first time Indian troops have crossed into West Pakistan in what is being seen as an act of war.
Since the first Indo-Pakistan war, both countries have continued to lay claim to the entire state of Kashmir. Currently Pakistan controls the smaller, northern sector of Azad Kashmir and the remaining area of Jammu and Kashmir, known commonly as Kashmir, is held by India.
Details of today's invasion are sketchy. There have been reports of the Indian Air Force in action, striking against military targets, including an oil tanker train, a group of military vehicles, a goods train carrying supplies, an army camp and some gun positions.
A spokesman for the Indian government said: "Our policy is that when Pakistan has bases from which it is mounting attacks on our territory we have to destroy those bases."
The Defence Minister Yashwantrao Chavan blamed recent attacks by Pakistani forces for the invasion.
Although there have been a number of air attacks against Indian installations in Punjab, these seem to have been mostly by single aircraft.
But Mr Chavan said: "It was quite apparent Pakistan's next move was to attack Punjab across the international frontier."
Reports from the Pakistani city of Karachi say forces have beaten back the Indian Army from Lahore.
They said advances at the border towns of Jasar, Wagah and Bedian had all been "fully stopped".
Pakistani officials say the number of Indian dead in the Lahore sector is 800, their own casualties are reported to be "very light".
The Pakistani President Ayub Khan has made an emergency broadcast to the nation saying, "We are at war".
He said the Indian attack was proof of the evil intentions which India had always harboured against Pakistan.
Reports from Delhi say Pakistani paratroopers have landed in the Punjab. Small groups have dropped in three places, Pathankot, Patiala and Ambala in an apparent attempt to damage military installations.
After three weeks of warfare both countries agreed to a UN-sponsored ceasefire.
In January 1966 they met at Tashkent and signed a declaration agreeing to resolve their dispute by peaceful means. They also agreed to withdraw to their pre-August positions.
It meant Pakistan retained control of the northern third of the state while India held the larger, southern and eastern section.
In 1972 the ceasefire line was renamed the Line of Control. Ever since this time most analysts believe India would accept the line to become the internationally-recognised boundary.
But Pakistan remains opposed to this idea as it would leave the predominantly Muslim Kashmir Valley as part of India. It also takes no account of Kashmiris who would like the whole state to be given its independence.
In 1989 armed resistance in Kashmir erupted against the Indian authorities. Pakistan supported the Kashmiri insurgents, leading to a further deterioration in relations between the two sides.
Throughout the early 1990s there were numerous uprisings against the Indian government.
In May 1999 the conflict reached a head again as India launched air strikes against Pakistani-backed Kashmiri militants.
Indian and Pakistani foreign ministers began a new series of talks in September 2004 aimed at resolving the Kashmiri dispute diplomatically.
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