Endowed with the Amazon and other mighty rivers, an array of huge dams and one-eighth of the world’s fresh water, Brazil is sometimes called the “Saudi Arabia of water,” so rich in the coveted resource that some liken it to living above a sea of oil.

But in Brazil’s largest and wealthiest city, a more dystopian situation is unfolding: The taps are starting to run dry.

As southeast Brazil grapples with its worst drought in nearly a century, a problem worsened by polluted rivers, deforestation and population growth, the largest reservoir system serving São Paulo is near depletion. Many residents are already enduring sporadic water cutoffs, some going days without it. Officials say that drastic rationing may be needed, with water service provided only two days a week.

Behind closed doors, the views are grimmer. In a meeting recorded secretly and leaked to the local news media, Paulo Massato, a senior official at São Paulo’s water utility, said that residents might have to be warned to flee because “there’s not enough water, there won’t be water to bathe, to clean” homes.

“We’re witnessing an unprecedented water crisis in one of the world’s great industrial cities,” said Marússia Whately, a water specialist at Instituto Socioambiental, a Brazilian environmental group. “Because of environmental degradation and political cowardice, millions of people in São Paulo are now wondering when the water will run out.”

For some in this traffic-choked megacity of futuristic skyscrapers, gated communities and sprawling slums, the slow-burning crisis has already meant no running water for days on end.

“Imagine going three days without any water and trying to run a business in a basic sanitary way,” said Maria da Fátima Ribeiro, 51, who owns a bar in Parque Alexandra, a gritty neighborhood on the edge of São Paulo’s metropolitan area. “This is Brazil, where human beings are treated worse than dogs by our own politicians.”

Some residents have begun drilling their own wells around homes and apartment buildings, or hoarding water in buckets to wash clothes or flush toilets. Public schools are prohibiting students from using water to brush their teeth, and changing their lunch menus to serve sandwiches instead of meals on plates that need to be washed.

Officials are promising ambitious solutions, like new reservoirs. But they are a long way off, and many people in this vast metropolitan region of 20 million are frightened by forecasts at Brazil’s natural disaster monitoring service that São Paulo’s main reservoir system could run dry in 2015.

Experts say the origins of the crisis go beyond the recent drought to include an array of interconnected factors: the city’s surging population growth in the 20th century; a chronically leaky system that spills vast amounts of water before it can reach homes; notorious pollution in the Tietê and Pinheiros rivers traversing the city (their aroma can induce nausea in passers-by); and the destruction of surrounding forests and wetlands that have historically soaked up rain and released it into reservoirs.

Deforestation in the Amazon River basin, hundreds of miles away, may also be adding to São Paulo’s water crisis. Cutting the forest reduces its capacity to release humidity into the air, diminishing rainfall in southeast Brazil, according to a recent study by one of the country’s leading climate scientists.

Officials also point to global warming. “Climate change has arrived to stay,” Geraldo Alckmin, the governor of São Paulo State, said this month. “When it rains, it rains too much, and when there’s drought, it’s way too dry.”

Shrinking water supplies are afflicting Rio de Janeiro and Minas Gerais, two other powerful states, while some smaller cities in the region are canceling Carnival festivities this week over worries about the lack of water to clean trash-strewn streets after celebrations.

But São Paulo’s crisis is particularly acute. Officials at Sabesp, the water utility controlled by São Paulo State, have acknowledged lowering the water pressure in the distribution network. While that effectively reduced the amount of water flowing through the system, the authorities have frequently insisted it is not the same as rationing, sowing confusion and anger among those unable to get water.

The water utility says it is pursuing a grandiose project to draw water from a nearby river basin and the construction of new reservoirs, though some efforts are not expected to be completed until well into next year.

“It’s a water system which clearly hasn’t been managed well,” said Newsha Ajami, director of urban water policy at the Stanford Woods Institute for the Environment, who recently met with water authorities here. “They’re going for these megaprojects, which should be the last solution,” when aggressive measures should have been taken months ago “to reduce consumption and leakage.”

More than 30 percent of the city’s treated water is estimated to be lost to leaks and pilfering. In a statement, the water utility said it was seeking to reduce leaks. It has been offering discounts to reduce consumption, while starting to impose steep fines this month on high water use.

Outright rationing — in which service would be cut entirely for certain periods, not just reduced — is “still under discussion and study,” said Sabesp, the water utility, after rains in recent weeks slightly raised reservoir levels. But for people already experiencing what they describe as de facto rationing, the position of the authorities has been perplexing, at best.

“I feel hatred, hatred of the governor and of Sabesp,” said Márcia Oliani, 54, the finance manager of an art gallery who endured six days without water in her apartment. “I’d like to take them out and set fire to them. They completely failed to warn us, and have just continued to lie about this throughout.”

Water specialists warn that the crisis could still be in its early stages, meaning that the shortages in São Paulo, Brazil’s economic capital, could hamper efforts to strengthen a sluggish national economy grappling with low prices for the commodities Brazil exports.

“They haven’t hit the worst of it yet if they’re not trucking in water in large amounts,” said Steven Solomon, the author of “Water: The Epic Struggle for Wealth, Power and Civilization,” comparing the crisis with the situation in cities in India and Pakistan where residents go foraging for water or buy it on the black market from truck-size tankers.

In a country where abundant water is a source of national pride, where crystal orbs containing the water from more than 15 Brazilian rivers have been displayed in the grand Ipiranga museum here, the crisis has some questioning how Brazil’s mighty global city arrived at this point.

Ignácio de Loyola Brandão, a writer whose 1981 novel, “And Still the Earth,” imagined a São Paulo grappling with ecological degradation and chronic water shortages, told reporters that he was not surprised at its water problems, citing the reluctance of many households to curb their own water consumption and what he called the nonchalance with which many people in Brazil treat scandals or natural disasters.

“The majority doesn’t get indignant with anything,” he said, “as if we’re comfortably strolling toward our own demise.”