The leaders of South Asian rivals India and Pakistan are to meet Friday on the sidelines of the U.N. General Assembly debate in New York. The meeting, and conciliatory remarks by both during their visit to New York, are being viewed as signs that the nuclear armed neighbors may be ready to put an end to nearly six decades of hostility.

Pakistani President Pervez Musharraf's General Assembly speech this week was devoid of the usual criticisms of India. The only reference to their dispute over Kashmir was a statement that he believes the two sides could resolve their differences through dialogue.

Indian Prime Minister Manmohan Singh followed on that theme Thursday in his Assembly address.

"It is known that since January of this year, India and Pakistan have initiated a composite dialogue to resolve all issues, including Jammu and Kashmir," he said. "I reaffirm our determination to carry forward this dialogue to a purposeful and mutual conclusion."

The conciliatory tone of both speeches has raised hopes of an easing of the tensions that have led to three wars since independence in 1947, two of them over Kashmir.

Speaking to reporters Thursday, President Musharraf said he is approaching his Friday meeting with Prime Minister Singh with a positive attitude, but no expectations of a breakthrough.

"I look forward to a constructive dialogue, but more than that I look forward to developing an understanding between ourselves," he noted. "We are meeting for the second time. After all, he's been born in Pakistan and I've been born in India. So there's a good ground for understanding."

The Pakistani leader called his meeting with his Indian counterpart critical, because the conflict over Kashmir had stifled progress and caused untold suffering in South Asia.

"We are two angry countries," he said. "Let's resolve the cause of that anger, and then only can we proceed on normalization everywhere. Yes, this whole area is suffering because of conflict between India and Pakistan. We are the two major countries of that region. In fact somebody has said 'When two elephants fight, the grass gets trampled, and we're trampling the grass everywhere around.'"

President Bush met with both the Indian and Pakistani leaders on the sidelines of the General Assembly, urging them to settle their differences over Kashmir. Secretary of State Colin Powell, who took part in the meetings, welcomed the resumption of dialog between the South Asian rivals.

"We did not get into the details of how the problem ultimately will be resolved concerning Kashmir, but we encouraged both sides to continue to talk to one another and carry this dialogue forward," said Mr. Powell. "We're encouraged that we now have open, honest, candid discussion on these very complex issues."

In addition to the three wars India and Pakistan have fought, the separatist insurgency in Indian Kashmir has killed an estimated 65,000 people since 1989.

The tensions have led U.S. officials in the past to describe South Asia as the world's most dangerous nuclear flashpoint.