Security for Mr Vajpayee's has been very high, but that didn't prevent a bomb explosion late at night in the Kashmiri summer capital, Srinagar, several kilometres from where he was staying.

No one was injured.

Speaking before the explosion, the Prime Minister reiterated his government's determination to keep Kashmir as a part of India despite the militant campaign and the claims of neighbouring Pakistan, which India accuses of fomenting the separatist violence.

The bomb didn't cause any injuries, but an investigation has begun into what has to be seen as a major lapse in security.

There was damage to surrounding buildings, and the fact that it was planted along the road to the guest house where the prime minister was staying is a significant embarrassment to the authorities in Kashmir.

Mr Vajpayee had earlier reiterated his government's intention of keeping Kashmir as a part of India and fighting against separatist militancy.

He also said he would not tamper with constitutional arrangements giving Kashmir more autonomy than an Indian state usually enjoys.

His party, the Hindu nationalist BJP, had long objected to that autonomy.

Mr Vajpayee also denounced intolerance and narrow-mindedness during a wide-ranging news conference in Srinagar, and said India could only work as a secular country where no religion or vision of culture was paramount.

On the second day of his trip, he is visiting a village near the cease-fire line that divides Indian and Pakistani-controlled parts of the territory.

The village was particularly hard hit by cross-border firing from the Pakistani side earlier this year.

Mr Vajpayee will also go to the southern part of Jammu and Kashmir, where Hindus are in the majority.

Little has changed in Kashmir since his government took office earlier this year.

Widespread militancy has been ebbing for some time now, but assassinations of members of the Indian security forces and bloody battles with small groups of militants still continue.

The elected government in Kashmir has taken over a degree of responsibility for fighting the militants, but the security forces remain deployed in large numbers.

India and Pakistan have been talking about their mutually-exclusive points of view on Kashmir, but making no progress.