Indian police said a group of nine arrived on the coast of southern Tamil Nadu state on Friday from northwest Sri Lanka.
The group included three children and three women and followed another batch of 24 Tamils, including seven women and nine children, who crossed the Palk Strait on Thursday.
Both groups left from Mannar on Sri Lanka's northwest coast.
The flight comes amid escalating violence that the government forces and rebels blame on each other.
A police official said the larger group has been lodged in a refugee camp near Rameswaram where about 650 refugees are already staying after tens of thousands of Tamils fled to southern India in the 1980s and early 1990s as Sri Lanka's two-decade civil war raged.
V Subramanian, the deputy superintendent of police, said: "On being questioned, these people said many more are waiting in Mannar to cross over to our coast. They said they fled their homes fearing death in the crossfire."
But officials in Sri Lanka, speaking after the first boat-load arrived, said the flight of refugees was an isolated incident.
Some officials in Mannar said that rumours of an exodus might be a propaganda ploy by the Liberation Tigers of Tamil Eelam (LTTE) to destabilise the area.
Fears of a return to a war that killed more than 64,000 people before a truce in 2002 are growing in tandem with deadly attacks by suspected rebels on the military and reported abuses by the armed forces against civilians.
Attacks on troops have increased markedly since the beginning of December and the authorities have blamed the Tigers, but the group has denied responsibility.
"On being questioned, these people said many more are waiting in Mannar to cross over to our coast. They said they fled their homes fearing death in the crossfire"
V Subramanian, the deputy superintendent of Indian police
Suspected Tigers killed nine sailors in a fragmentation mine ambush on a main supply route in Sri Lanka's north on Thursday, which came after similar ambushes killed 39 military personnel in December alone, many of them in Mannar.
Each recent attack on the military has also come on the heels of Tiger reports of army abuses and killings.
The Sri Lankan government has repeatedly said it will not be provoked into resuming war, but Mahinda Rajapakse, the new president, is having to juggle the demands of hardline allies who hate the Tigers and an increasingly frustrated military.