BALUKHALI, Bangladesh — Up to their ankles in mud, hundreds of Rohingya refugees fought to the front of the crowd outside of their makeshift camp. An open-bed truck full of Bangladeshi volunteers was passing by, tossing out donated goods at random: small bags of rice, a faded SpongeBob SquarePants T-shirt, a cluster of dirty forks.

Entire families sloshed through the rain hoping to grab whatever they could. One boy, no older than 6, squeezed his way to an opening where a pair of oversize men’s jeans came hurtling off a truck. He had to fight off an older boy before he could run off with the prize.

There were already more than 200,000 ethnic Rohingya migrants stuck in camps like this one, Balukhali, in southern Bangladesh. But over the past month, at least 500,000 more — more than half of the Rohingya population thought to have been living in Myanmar — are reported to have fled over the border to take refuge, surpassing even the worst month of the Syrian war’s refugee tide.

As international leaders squabble over whether to punish Myanmar for the military’s methodical killing and uprooting of Rohingya civilians, the recent arrivals are living in abjectly desperate conditions.