Desperate Tamil civilians are trying to flee to India in small boats to escape intensifying fighting between the Sri Lankan military and Tamil Tigers.

As Sri Lanka called yesterday for international help in dealing with tens of thousands fleeing fighting, the Guardian has learned that boat-loads of refugees have arrived in Tamil Nadu – and others have attempted the trip – to avoid internment in government-run camps. Aid workers say some boats have sunk and children have been washed overboard. Other fleeing the fighting have sailed along the coast to government-held areas.

Yesterday members of three families who made the perilous journey to India described their escape. In all, 13 of them slipped away in the middle of the night to avoid being spotted by the Liberation Tigers of Tamil Eelam rebels, who were reportedly shooting those fleeing.

They climbed into a boat belonging to Sivachandran Sivasnanam, a fisherman from Jaffna, who had persuaded the rebels to let him to take it out fishing.

"Day by day the shelling was getting worse. We were living in a bunker we had dug in the sand. There was shelling coming from the army area and the LTTE was shelling from inside the zone and sometimes they would come to take the boys as recruits," said Sinnathamby Ampumani, 48, a teacher.He spoke to the fisherman and decided to try to make it to India. It was 3.30am when Ampumani reached the shore with his family.

"We didn't take anything with us except for a few jewels and some money because if we had been seen other people would have informed on us," he said.

As quietly as they could, they pushed off. "We kept close to the shore for as long as we could and then headed into the open sea and turned left."

Eventually they spotted an Indian fishing boat, which gave them food and water and pointed them in the direction of the sub continent. Three hours later, they met a trawler. By this time, they had been travelling for most of the day and were almost out of fuel, Ampumani said.

"The trawler said it would tow us for a few hours and finally we saw the beach. We were so happy that we were safe."

Siva Kumar, 26, the brother of the boat's owner, said they had been afraid of running into Sri Lankan naval vessels, but in the end they saw none.

"They were staying about 3km [1.8 miles] off the shore because I think they were afraid of the Tigers," he said.

His brother, he said, had never been to India. But he had been confident of finding his way in the dark, even without a compass. "We knew which side was India and which was China," he said. Eleven of the group have been given identity cards and refugee status, but two remain under lock and key, including a young woman whose hands had been blown off in an explosion. According to local staff, the police suspect the pair of being LTTE members.

India is separated from Sri Lanka by the Palk Strait, which is only 28 miles across at its narrowest point, and others have clearly had the same idea as Ampumani's group. Another boat arrived earlier this week. Others have sailed across from Mannar and Jaffna, areas previously held by the LTTE but now in government hands. The refugees have paid boatmen to make the crossing: one apparently handed over 20,000 Sri Lankan rupees (about £120).

According to aid workers, there are 117 camps in Tamil Nadu housing about 70,000 refugees.

Sooriya Kumary, from the group OFERR, which is working with Christian Aid, said the refugees were risking their lives to make the sea journey because they feared being arrested and harassed by the authorities in Sri Lanka or having their children forcibly recruited by the LTTE.

"They feel safer in India," she said. "The vast majority are coming by boat. They are coming in flimsy fishing boats and it's a very dangerous crossing. Sometimes the boats capsize. The sea is very rough and sometimes women are not able to hold onto their children. Sometimes they just take too many people in the boat and they sink.

Yesterday Sri Lanka called for international help in dealing with the tens of thousands of civilians fleeing the fighting in what it said was an emergency humanitarian situation.