By S. Murari

CHENNAI, India, Oct 15 (Reuters) - A group of Indian lawmakers, whose support is crucial to the government, threatened to resign on Wednesday if India failed to stop the worsening conflict in Sri Lanka, officials said.

About 39 lawmakers, all allies of India's ruling Congress party-led coalition met in the southern city of Chennai on Wednesday and gave the Indian government two weeks to intervene or face being brought down, the lawmakers said.

The meeting was chaired by M. Karunanidhi, chief minister of Tamil Nadu state and leader of the Dravida Munnetra Kazhagam party (DMK), a key ally of the Congress party.

"The decision (to resign) applies to members of both houses of parliament from Tamil Nadu," Karunanidhi said after the meeting, without specifying the type of intervention they sought.

Sri Lankan troops stepped up their offensive against Tamil Tiger rebels fighting for a separate homeland this year and the government says its forces have killed thousands of the rebels since January.

India sent peacekeepers to the Island nation in 1987, only to withdraw them after losing more than 1,000 men in battle and facing allegations of human rights violations. India has since said it does not want to get involved in Sri Lankan politics.

Congress party leaders began voicing concern under pressure from their southern allies in Tamil Nadu, where the mainly Tamil population takes the view that Sri Lankan government troops are wiping out Tamils on the island.

On Wednesday, Prime Minister Manmohan Singh said India was concerned at the rising hostilities in Sri Lanka.

"The situation in Sri Lanka does not call for any military victory, it calls for a negotiated political settlement which respects the unity and integrity of Sri Lanka ... (and) the essential human rights of the minorities, particularly the Tamil minority," Singh told a new conference in New Delhi.

The Tigers have waged war since 1983 to create a homeland for Sri Lanka's minority Tamil people, and in doing so landed on U.S., E.U. and Indian terrorism lists for widespread bombings and assassinations of rivals, including Tamils.

In 1991, they were charged with killing India's former Congress Prime Minister Rajiv Gandhi. (Writing by Bappa Majumdar; editing by Philippa Fletcher)

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