Mr Vajpayee spoke from behind bullet-proof glass
India's Prime Minister Atal Behari Vajpayee has said his offer of talks with Pakistan is conditional on Islamabad stopping militant infiltration into Indian Kashmir.
During a rare public rally in the Kashmir capital, Srinagar, on Friday, Mr Vajpayee said he was ready to extend his hand of friendship to Pakistan.
Pakistan's Prime Minister Zafarullah Jamali welcomed the overture, saying it was a "positive development".
The dispute has remained at the heart of differences between India and Pakistan for over 50 years.
Addressing a press conference in Srinagar on Saturday, Mr Vajpayee said the government would learn from previous mistakes.
He said that elections held in Indian-administered Kashmir had sometimes been manipulated in the past.
At the same time, he stressed that last year's state elections - which led to the defeat of his allies - had been free and fair.
The prime minister also announced an economic package:
100,000 jobs would be created in the next two years.
a special task-force set up to prepare employment-generating schemes
soft loans for 1,200 house-boats owners and 500 hoteliers
Overture to Pakistan
Mr Vajpayee was speaking one day after offering to hold talks with Pakistan to resolve the Kashmir dispute.
Mr Vajpayee said on Friday that dialogue was the only way to bring peace in Kashmir.
Our correspondent in Islamabad, Zaffar Abbas, says the two leaders are hoping to cool tempers following a series of highly provocative statements from both sides.
"Pakistan's stand remains the same. But once talks start there... could be flexibility from both sides," Mr Jamali told reporters in Islamabad.
Heavy security has surrounded Mr Vajpayee's visit to Srinagar, where a protest strike by separatists had closed most of the city.
"We have come to share your pain and grief," the prime minister told 20,000 people at Friday's rally, many of them bused in by the authorities.
"Guns will not solve the matter, but brotherhood will," he said from behind bullet-proof glass.
Mr Vajpayee also promised to provide more jobs and assistance for the Kashmiri people and said he was fully behind the state's new government.
The new administration of Mufti Mohammad Sayeed won office by promising to fight separatism by improving living conditions.
The prime minister also endorsed the "healing touch" policy of the Mr Sayeed's government.
But he said the policy has to be implemented carefully lest it should have a reverse effect.
"There is no healing touch for terrorists. If they want to talk, doors are open for them," he said.