A fresh exodus of Tamil refugees fleeing a Sri Lankan Army offensive in the island's strife-torn northern provinces in the last week has stretched relief camps in south India to the breaking point, Indian officials and Tamil refugee sources said today.

Indian officials said that 500 to 600 boat refugees were crossing the narrow Palk Strait from Sri Lanka to Rameswaram, on the coast of the south Indian state of Tamil Nadu, each day, representing a 10-fold increase in arrivals. On Saturday alone, a record 780 families arrived, according to district official S. Gurumurthi.

Tamil exiles living in Madras and interviewed by telephone said that hundreds of civilians in the Jaffna and Mannar districts of northern Sri Lanka were hiding in the jungle while waiting for an opportunity to escape.

"If this flow keeps up, there will be nobody left there except the young militants," said Vettivelu Yogeswaran, a Madras-based Tamil exile and former member of the Sri Lankan parliament. He was referring to the separatist insurgents who are fighting a guerrilla war to carve an independent Tamil state in the northern quarter of Sri Lanka.

Official sources said that since the Sri Lankan Army began a new sweep through the north two weeks ago, the population of a refugee camp at Mandapam, near Rameswaram, had swelled to 5,000, far exceeding the camp's capacity.

Government officials estimate that 40,000 identified Tamil refugees are now living in Tamil Nadu, but say that the actual figure is much higher because many refugees move in with relatives on the mainland without registering with the authorities. The Tamil Eelam information center in Madras estimates that 200,000 Sri Lankan Tamils are living in south India.

The most recent census, in 1981, counted 792,200 Tamils and 4,600 Sinhalese in the Jaffna Peninsula, but virtually all Sinhalese, who comprise 74 percent of the island's total 15 million population, have left. Taking into account Tamils who have emigrated to the United States and Europe since anti-Tamil rioting in July 1983 left more than 400 dead, the population of Jaffna is believed to have dropped below 600,000.

Appapillai Amirthalingham, secretary general of the mainstream Tamil United Liberation Front, said in a telephone interview from Madras that most of the new refugees are coming from Mannar, on Sri Lanka's west coast, and the area of Mullaittivu, on the east coast, both of which have been the object of Army offensives recently.

On Feb. 11, Amirthalingham said, many of the refugees returned to their villages to harvest their rice paddies and were trapped there when a Sri Lankan Army unit went on a rampage of vengeance killings in which 60 Tamils died. The Sri Lankan government version is that the Army raided a major guerrilla base and arms cache, killing 58 armed Tamils.

Three boats carrying more than 100 refugees from Pesalai were fired upon early today by a Sri Lanka naval vessel, forcing it to change course from Rameswaram and land at Dhanushkodi, 12 miles away, the United News of India reported.