GENEVA — United Nations officials struggling to mobilize aid for more than half a million Rohingya Muslims who fled violence in Myanmar in recent weeks have reported another surge of arrivals in Bangladesh, and warned on Tuesday that the crisis could worsen.

More than 11,000 people crossed the border into Bangladesh on Monday, the United Nations refugee agency said, and thousands more are waiting to cross.

More than 515,000 Rohingya have fled to Bangladesh since Aug. 25, when Myanmar’s army responded to attacks by militants in the western state of Rakhine by burning whole villages in a campaign that the United Nations has called ethnic cleansing.

The number of people crossing the border had slowed to around 2,000 a day in the past week. But Adrian Edwards, a spokesman for the refugee agency, told journalists in Geneva on Tuesday, “We’re back in a situation of full alert as far as influxes are concerned.”