COX’S BAZAR, Bangladesh — Thousands of Rohingya Muslims from Myanmar sought refuge in Bangladesh on Monday, in a new surge in an unrelenting flow of people driven by violence the United Nations has denounced as ethnic cleansing and increasingly by hunger too.

Reporters on the Bangladeshi side of the border, in Palong Khali district, saw several thousand people crossing from Myanmar’s Rakhine State, filing along embankments between flooded fields and scrubby forest.

“Half of my village was burned down. I saw them do it,” said Sayed Azin, 46, who said he had walked for eight days with his 80-year-old mother in a basket strung on a bamboo pole between him and his son.

Soldiers and Buddhist mobs had torched his village, he said.

“I left everything,” he said, sobbing. “I can’t find my relatives ... I can’t take this any more.”

Some new arrivals spoke of bloody attacks by Buddhist mobs on people trekking toward the border.

About 519,000 Rohingya have fled Myanmar since Aug. 25, when attacks by Rohingya militants on security posts in Rakhine State sparked a ferocious military response.

Refugees and rights groups say the army and Buddhist vigilantes have engaged in a campaign of killing and arson aimed at driving the Rohingya out of Myanmar.

Myanmar rejects accusations of ethnic cleansing and has labeled the militants from the Arakan Rohingya Salvation Army who launched the initial attacks as terrorists who have killed civilians and burnt villages.

Among those fleeing were up to 35 people on a boat that capsized off the Bangladesh coast on Sunday. At least 12 of them drowned while 13 were rescued, Bangladeshi police said.

“We faced so many difficulties, for food and survival,” survivor Sayed Hossein, 30, told Reuters, adding that his wife, three children, mother and father in law had drowned.

“We came here to save our lives.”

The Myanmar government has said its “clearance operations” against the militants ended in early September and people had no reason to flee. But in recent days the government has reported large numbers of Muslims preparing to leave, with more than 17,000 people in one area alone.

The government cited worries about food and security as their reasons.

Some villagers in Rakhine State said food was running out because rice in the fields was not ready for harvest and the state government had closed village markets and restricted the transport of food, apparently to cut supplies to the militants.

“The situation’s getting worse, we have no food and no guarantee of security,” said a Rohingya resident of Hsin Hnin Pyar village on the south of the state’s Buthidaung district.

He said he knew of several people who had been picked up by police and beaten on suspicion of having militant links, adding that a lot of people were preparing to flee.

Senior state government official Kyaw Swar Tun declined to go into details when asked about the food situation, except to ask, “Have you heard of anyone dying of hunger in Buthidaung?”

The reports of food shortages will add to the urgency of calls by aid agencies and the international community for unfettered humanitarian access to the conflict zone.

The insurgents declared a one-month ceasefire from Sept. 10 to enable the delivery of aid but the government rebuffed them, saying it did not negotiate with terrorists.