India and Pakistan hailed progress in diplomatic ties on Thursday, promising to open a new chapter in their fraught relationship at a next round of formal peace talks due to take place by the end of this month.

Lasting peace between the nuclear-armed rivals is seen as essential to South Asian stability and to helping a troubled transition in Afghanistan as NATO-led combat forces plan their military withdrawal from that country in 2014.

Indian Prime Minister Manmohan Singh and his Pakistani counterpart Yusuf Raza Gilani held nearly an hour-long discussion at a resort island in the Maldives, punctuating a recent thaw between the two.

That includes Pakistan's decision to grant its giant neighbour favourable trade terms and end huge restrictions that require most products to move via a third country.

The next round of talks will be more positive, more constructive and will open a new chapter in the history of both countries, Gilani told reporters after the meeting with Singh on the sidelines of a summit of South Asian leaders.

I can only assure you that I discussed all core issues.

Pakistan Foreign Minister Hina Rabbani Khar told Reuters that the next round of talks would begin by the end of this month.

India and Pakistan, which have fought three wars since independence from Britain in 1947, resumed a peace dialogue in February that was derailed after an attack by Pakistan-based militants in the Indian city of Mumbai in 2008.

We will resume this dialogue with the expectation that all issues which have bedevilled relations between the two countries will be discussed, Singh said. The time has come to write a new chapter in the history of the relationship of the two countries.

Progress has been slow and Singh acknowledged that more needed to be done.

Every time we have met, we have held very extensive discussions of relations of the two countries. These have yielded some positive results, but more needs to be done.

TRADE TO BE NORMALISED

The two leaders, who last met in March at an international cricket match in India, discussed border disputes, sharing of common river water, Kashmir, militancy and trade, Gilani said.

Pakistan last week said it would grant India most-favoured nation trade status. India gave the status to Pakistan 15 years ago, and the state of trade has closely been linked to the political temperature between the two.

The process of trade normalisation will be taken to its logical conclusion and we would also move towards a preferential trade agreement with Pakistan... and a liberalised visa regime, Indian Foreign Secretary Ranjan Mathai told reporters, referring to visas for business people.

A judicial panel from Pakistan is due in India shortly to investigate the Mumbai attacks that killed 166 people, including speaking with the lone surviving gunman, Mohammad Ajmal Kasab, Pakistani Interior Minister Rehman Malik said.

An Indian court convicted Kasab, a Pakistani national, of murder and other charges, and he is appealing a death sentence.

He is a terrorist. He is a non-state actor. He should go to the gallows, Malik told reporters.

India has demanded Pakistan investigate and convict the militants on its soil responsible for the assault on the Indian commercial capital.

Pakistani authorities have put seven members of the Lashkar-e-Taiba group on trial but India says Pakistan needs to do more.

The leaders are in the Maldives for a summit of the eight-nation South Asian Association for Regional Cooperation (SAARC), which also includes Bangladesh, Bhutan, Afghanistan, Sri Lanka, Nepal and the host country, an archipelago of nearly 1,200 mostly uninhabited atolls in the Indian Ocean.

(Writing by Bryson Hull; Editing by Yoko Nishikawa)