"The time has come to leave behind the animosities and the misgivings of the past and to think the unthinkable of moving together in pursuit of our common objective of getting rid of chronic poverty, ignorance and disease," said Manmohan Singh, India's prime minister.
"I make this offer to the people of Pakistan on this historic occasion," Singh said in Amritsar before inaugurating a new bus service between the two countries.
"I am sure the leadership of Pakistan will reciprocate."
Singh said India was committed to the peace process, adding that it could bring enormous economic benefits to the people of both sides. And there was a growing recognition in both countries that "terrorism is an enemy of civilised societies".
"General (Pervez) Musharraf has taken concrete steps to curb terrorism and I compliment him for that. But more needs to be done in the interest of both India and Pakistan," Singh said, referring to the Pakistani president.
"I have often said that borders cannot be redrawn but we can work towards making them irrelevant -- towards making them just lines on a map"
Indian Prime Minister
The bus service links the holiest site of the Sikh religion, Amritsar and its Golden Temple, with Nankana Sahib in Pakistan, the birthplace of the religion's founder, Guru Nanak.
Singh called it another step on the road to peace between the nuclear-armed rivals, and a day of hope for the divided state of Punjab, scene of hundreds of thousands of deaths in riots during the partition of the subcontinent in 1947.
Relations between India and Pakistan have improved since peace talks were launched in 2004 but there has been little progress in solving their core dispute over Kashmir.
Singh said it was a mistake for Pakistan to link normalisation of other relations to finding a solution to the dispute over the Himalayan region.
"But we are not afraid of discussing Jammu and Kashmir or of finding pragmatic, practical solutions to resolve this issue as well," he said, recommending a step-by-step approach.
Singh said both sides should begin a dialogue with people in the parts of Kashmir they control.
"I have often said that borders cannot be redrawn but we can work towards making them irrelevant -- towards making them just lines on a map," he said.
Kashmir has been at the core of
He also suggested the two parts of Kashmir could work out "cooperative, consultative mechanisms" to secure the social and economic development of the region.
His words received a lukewarm welcome from Kashmir and the head of the moderate wing of the separatist All Parties Hurriyat Conference, Mirwaiz Umar Farooq. He told Reuters much more was needed than confidence-building measures.
"If the prime minister is sincere he should announce demilitarisation in Kashmir, stop human rights violations and find a solution of the problem in accordance with the wishes of the people of Jammu and Kashmir," Farooq said.
India accuses Pakistan of supporting Islamic fighters in Kashmir, the cause of two of three wars between the neighbours. More than 45,000 people have died since the Kashmir revolt broke out in 1989, Indian officials say.