Some 370 of the dead were from Bombay - the city Indians know by the name Mumbai - and the surrounding area in Maharashtra state.
India's financial hub was pounded by two days of unusually heavy monsoon rains this week, including one day marked the heaviest single day of monsoons in India since record keeping began a century and a half ago.
A stampede set off by rumors of a dam bursting late Thursday also killed at least 15 people and injured more than 25 in an outlying Bombay shantytown, said R.R. Patil, deputy chief minister of the province surrounding Bombay, Maharashtra state.
Residents of the Nehru Nagar slum panicked after hearing the rumors and after landslides in another Bombay shantytown had buried dozens of people alive, mostly young children and old people too slow to escape a collapsing hillside.
Many of the stampede victims were also children. "People died due to false rumors," Patil said. "Fifteen people have been killed and seven are children."
He said police vans with loudspeakers had been deployed to stem the panic in a city already strained by the flooding. The rains shut down much of the city, including the Bombay Stock Exchange.
On Friday, dozens of new bodies were found, pushing the death toll to 696, officials said. Alongside their work in Bombay, rescuers fanned out to vast areas in the western Maharashtra state also hard hit by the monsoons, said N. Nayar, an official at the government's emergency control room.
In Bombay, most victims drowned, were crushed by falling walls, or were electrocuted by stepping on exposed wires.
Residents responded to the devastation by opening their homes and distributing food to motorists stuck in traffic and people wading through knee-deep water.
"They were just angels. Women and children were giving food, biscuits to people on the road and even assuring us that it was home-cooked," said G. Sawant, a manager at a private infrastructure company.
The rain began Tuesday, when the cosmopolitan city that is home to India's financial and movie industries was hit by up to 37 inches in some areas, the highest recorded one-day total. Much of it came over a few evening hours Tuesday, transforming roads into rivers. The rains trailed off by Thursday, leaving an overcast sky.
India's previous heaviest rainfall, recorded in the northeastern town of Cherrapunji on July 12, 1910, was 33 inches, according to the Indian Meteorological Department.
In one shantytown north of Bombay this week, relief workers and survivors searched the ruins of makeshift homes crushed when a water-soaked hill collapsed on top them. While the complete toll from the landslide in the Saki Naka neighborhood was unclear, at least 110 people were killed, and more than 45 others were missing and presumed dead.