A breach in the wall of the 118-year-old Jaswant Sagar Dam in Jodhpur district flooded the Luni river and authorities sounded an alert in Jodhpur, Pali, Barmer and Jalore districts, said Kiran Soni Gupta, the top district administrator.
Nearly 20,000 people evacuated their homes and moved to higher ground, while air force helicopters dropped food packets over two nearly submerged villages on Sunday, Gupta said.
India's monsoon rains, which began a month ago, have killed 107 people in Gujarat state and 48 in Maharashtra state - both in the west of the country - and 22 in northwestern Rajasthan state, officials said.
Parts of Bilara, a town 200 kilometers (125 miles) west of Jaipur, and some villages near the breached dam were up to six feet (1.83 meters) under water, said C. K. Matthew, a principal secretary in charge of Rajasthan's crisis management and relief work.
"The danger seems to be over as the water discharge from the dam has receded. But we are still on high alert and monitoring the situation," Gupta told The Associated Press on Monday.
Pali, an industrial town, recorded 324 millimeters (12.76 inches) of rain on Friday, surpassing the 28-year-old record of 305 millimeters (12 inches) of rain for one day, the state meteorology department said.
Two people were electrocuted there over the weekend, Matthew said. Two others drowned in Rajasthan's Barmer district.
Nearly 500 Indian and Pakistani passengers were stranded for nearly two days at Jodhpur railroad station as flooding of the rail track near Tilwara, a border village prevented the Pakistan-bound Thar Express from leaving Saturday, said Y. K. Sharma, a railroad spokesman. The train finally departed for Pakistan on Monday.
The situation in the western states of Gujarat and Maharashtra improved over the weekend with no heavy rains and flood waters receding from most areas.
The monsoon season in India runs from June to September. More than 800 people died last year, with most deaths blamed on drowning, landslides, house collapses or electrocution.