The meeting between Indian Prime Minister Atal Bihari Vajpayee and Pakistani President Pervez Musharraf in Islamabad has raised hopes that the two nations may seek new ways to end years of hostility.

Just a few days ago, Indian officials downplayed suggestions that Prime Minister Vajpayee would meet privately with Pakistan's President Pervez Musharraf.

The two men, however, met for the first time in more than two years Monday on the sidelines of the summit meeting of the South Asian Association for Regional Cooperation in Pakistan.

Sukh Deo Muni, from Jawaharlal Nehru University in New Delhi, said there were signs that Mr. Vajpayee was ready to take a big step. "He repeatedly says that this is the last chance, and 'in my lifetime, I want to do something,'" said Mr. Muni. "Maybe the creating history bug has caught on to him - and if that is so, there is nothing which you cannot expect."

Mr. Vajpayee has indicated his goal is to build a more peaceful relationship with India's historical rival, Pakistan.

They have fought three wars, two of them over the border region of Kashmir, which the two governments claim in its entirety.

India and Pakistan broke off relations after militants attacked India's Parliament in 2001. New Delhi accused Islamabad of involvement in the attack, which Pakistan denied. The incident almost sparked another war, this time between two nations that had become nuclear powers.

But there was no angry rhetoric on Monday. Speaking just before meeting Mr. Musharraf, Prime Minister Vajpayee took a conciliatory tone. He said it is necessary that India and Pakistan have adequate representation and that dialogue goes on continuously, that they understand each other's difficulties and find a way out together.

The regional summit comes on the heels of a series of peace measures between India and Pakistan. The two sides have resumed diplomatic relations, restarted transportation links and ordered a cease-fire along Kashmir's frontline.

Ending tensions between India and Pakistan may still be a long way off, because the Kashmir dispute is about more than just territory. Analysts say that, as India's only Muslim-majority state, Kashmir has become critical to the nation's identity.

"If two million Muslims are allowed to secede from India on the grounds of religion, what will happen to the other 160 million Muslims scattered across the length and breadth of India?' asked Brahma Chellaney of the Center for Policy Research, a New Delhi think-tank. "What will happen to the secular fabric of India? Will India remain a secular and democratic Indian state? Kashmir is not just a territorial issue for India."

In a briefing to reporters, India's Foreign Minister Yaswant Sinha said that Mr. Vajpayee also congratulated the Pakistani president on the successful summit. But Mr. Sinha refused to confirm reports that India and Pakistan would issue a joint statement about their on the meeting.