SAHARSA DISTRICT, India — Hungry villagers rioted, desperate families swam for their lives, and chaos spread across a wide swath of flooded plains in northern India today as authorities mounted one of the country’s largest relief efforts.

Soldiers and aid workers scrambled to reach hundreds of thousands of people still stranded on rooftops, trees and specks of dry land more than two weeks after monsoon rains caused the Kosi River to burst its banks and turn hundreds of square miles of Bihar state into a giant lake.

The road linking Saharia village to the rest of the hard-hit Saharsa district washed away yesterday. Those who could braved the fast-flowing, neck-deep water, carrying bicycles above their heads, and bags of clothes on their shoulders. Some swam out into the stream, dragging frightened cattle after them.

“The water came on Saturday, and since then no government officials have come to us,” a Saharia resident, Ram Bachan Rai, 60, said.

The army sent more than 5,000 soldiers to join rescue efforts, while officials said more than half of the 1.2 million stranded had been rescued. Officials did not yet have a precise tally of those killed by the flooding, but estimates ranged from dozens to thousands.

The relief effort was the first to deploy all three branches of India’s military — the army, navy, and air force, a top disaster management official in Bihar, Prataya Amrit, said. With the extra forces, officials hoped to complete the rescue phase of operations in two days, Amrit said.

But even as attention turned to housing and feeding the refugees, relief efforts were haphazard amid the chaos. New areas were cut off, posing fresh challenges to rescuers. Strong currents hampered their work, with the military being extra cautious after one of its boats capsized over the weekend, killing 19 people.

Though residents of Saharia village said no government officials had come to their aid, they were visited by relief workers from UNICEF and the European Union.

“We are going from place to place trying to assess the needs of the people, see what gaps there are and how we can fill it,” Malini Morzaria, of the EU’s aid department, said as she waded through knee-deep water to reach an isolated hamlet.

Near Saharia, the government set up a camp in a school, where some 1,000 people huddled with their cattle and goats.

The refugees were getting shelter, medical treatment and three meals a day of cooked rice and lentils. There was a pump with clean water where mothers were vigorously scrubbing the flood waters off their children.

However, there was not enough room for everyone. Some refugees camped under a large tree, while others staked a claim to a nearby gas station.

“Influential people are taking all the relief materials,” one of those living under the tree, Rajendra Sah, 43, complained.

As frustration grew among the homeless, crowds attacked government offices and there were reports of looting.

At Madhepura, one of the biggest flooded towns, residents stormed a government office late yesterday throwing stones and demanding food, television news reports showed.

At Saharia, a man said thugs had stolen his family’s vital supplies. “People came in a boat and took away the grain we had stored on the roof,” said Chetu Yadav, 28. “They were armed so we were afraid to challenge them.”

With the numbers in the camps for the displaced expected to nearly double in the coming days, there were fears that crowded and unsanitary conditions could lead to outbreaks of diseases such as cholera.

Officials say the flooding is expected to continue until November, when the last of the monsoon rains taper off. Only then will workers be able to plug the breach in the Kosi River that is more than a mile wide and growing.

The river, which flows down from the Himalayas into India where it joins the Ganges River, dramatically changed course after the breach, moving dozens of miles to the east and inundating hundreds of square miles.

The monsoon season, which starts in June, brings rain vital for the farmers of South Asia but also can cause widespread destruction.

At India’s northeastern state of Assam, floods have submerged roughly 1,500 villages, drowned 15 people, and displaced hundreds of thousands, the state’s relief minister, Bhumidhar Barman, said. State authorities were working hard to reach affected areas, Mr. Barman said.

Two of Assam’s major rivers, the Brahmaputra and the Barak, were flowing above the danger levels at more than a dozen places, according to a bulletin issued by the Central Water Commission, a federal flood monitoring agency.

At neighboring Bangladesh, flooding cut off at least 50,000 people, news reports said. A flood warning agency said the situation was “likely to deteriorate.” News reports said three people drowned Monday in flood-ravaged areas north of the capital, Dhaka.