ACROSS the border, inside Myanmar, columns of smoke can be seen rising at dawn; each evening dusk reveals the fires at their bases. All week villages have been burning in northern Rakhine state, home of the Rohingyas, a persecuted Muslim minority. Refugees have been fleeing to Bangladesh across rice paddies, along muddy mountain paths and in boats over the Naf river, which divides the two countries. They are fleeing systematic violence from the Burmese army and armed mobs of Rakhines, another local ethnic group. The UN has counted 164,000 who have already arrived in Bangladesh; many more are thought to be on their way.

At the end of the Myanmar-Bangladesh Friendship Road, backed against the border fence near the town of Ghumdum, is a rapidly growing, makeshift camp holding some 5,000 new refugees. A Bangladeshi border guard points to a nearby hillock where a fire is raging; he says the Burmese army is burning down houses. Nurul Islam, a 30-year-old farmer, says he left his home in Razabil village in Myanmar last week when soldiers opened fire on villagers and set the houses on fire. Women and men were separated. Soldiers raped his 13-year-old sister Khadiza; mobs of Rakhines armed with swords mutilated her body. His father was also killed.

Fatima Khatun managed to escape her burning village and arrived in Bangladesh on September 4th with eight members of her family. She says many children and old people died on the week-long trek through the muddy monsoon-soaked hills. When she and others crossed a river inside Myanmar by clinging to bamboo rafts, soldiers opened fire on them. Many more villagers are hiding in Myanmar or have lost their way, she says.

At a nearby petrol station, Mohammad Jahangir explains that he has just arrived from the town of Taung Bazaar after a 13-day march. He is carrying his 8-year-old son, who cannot walk because of a bullet wound on his right leg.

Matthew Smith of Fortify Rights, an NGO, says that based on copious, detailed testimony from many witnesses, “We can now say with a high level of confidence that state-led security forces and local armed residents have committed mass killings.” It looks, says Mr Smith, as if the Burmese army is trying to drive all Rohingyas out of the country. Fortify Rights has documented many cases of indiscriminate killing, rape, mutilation and other crimes.

To the south of Ghumdum, at another border crossing, locals reckon 5,000 refugees have arrived that morning alone. One member of the exhausted procession is Sawza (who goes by one name), a health worker from the town of Buthidaung. She left her home on August 25th, the day the Burmese army went on the rampage in response to attacks by Rohingya militants that killed 12 policemen. At first, Sawza thought it would be safe for her family to stay. But when she heard that Zabar Khalimullah, a wealthy local, had been killed, she decided to flee. Unlike during another bout of violence last year, affluent landowning Rohingyas are leaving this time. Sawza says that during her 15-day journey she saw parents forced to abandon children who were too weak to keep walking and a man in his 50s who had to leave his 80-year-old father by the wayside.

Even farther south, on the beach at Shah Porir Dwip, the southernmost tip of Bangladesh, Roshida Begum climbs out of a wooden boat with a few belongings and what is left of her family. Burmese soldiers took away her daughters, who were 16 and 22, she says. She later found their mutilated bodies. Her husband was also killed. Farther along the beach is another group of 30 or so Rohingyas, who spent five days hiding in the hills before crossing to Bangladesh. Obaida Khatun, the oldest woman in the group, says that three of the young women with her were raped.

The narrow strip of Bangladesh that juts into the Bay of Bengal alongside Myanmar already hosts hundreds of thousands of Rohingya refugees from previous exoduses, in 1978 and 1991-92. They compete with locals for food, firewood, land and jobs. It is the poorest part of Bangladesh. Literacy in the region is 27%. Aid is arriving in dribs and drabs—food, water purifiers, tarpaulins—but not nearly enough. Among the throngs of refugees looking for shelter in the area this week was Zainab Begum, whose father was killed by Burmese soldiers. “Everything has turned to ashes,” she says.