People walk down a flooded street in Houston, Texas, as they evacuate their homes Monday because of Hurricane Harvey. Harvey is expected to dump up to 40 inches of rain on Texas over the next couple of days. (Joe Raedle/Getty Images)

Floodwaters reached the roof lines of single-story homes Monday, and people could be heard pleading for help from inside as Hurricane Harvey kept pouring rain on the Houston area after a chaotic weekend of rising water and rescues.

The nation’s fourth-largest city was still largely paralyzed, and there was no relief in sight from the storm that spun into Texas as a Category 4 hurricane, then parked itself over the Gulf Coast. With nearly two more feet of rain expected, authorities worried whether the worst was yet to come.

Harvey has been blamed for at least three confirmed deaths, including a woman killed Monday in the town of Porter, northeast of Houston, when a large oak tree toppled onto her trailer home.

The disaster unfolded on an epic scale in one of America’s most sprawling metropolitan centers. The Houston metro area covers about 10,000 square miles, an area slightly bigger than New Jersey. It’s crisscrossed by about 1,700 miles of channels, creeks and bayous that drain into the Gulf of Mexico, about 50 miles to the southeast from downtown.

On Monday, the city’s normally bustling business district was virtually deserted, with emergency vehicles making up most of the traffic. Most traffic signals were out, and most businesses closed.

Elsewhere, water gushed from two reservoirs overwhelmed by Harvey as officials sought to release pressure on a pair of dams where floodwaters were at risk of spilling from around the sides of the barriers. The move aimed at protecting the downtown business district risked flooding thousands more homes.

Meanwhile, rescuers continued plucking people from the floodwaters — at least 2,000 so far, according to Houston Police Chief Art Acevedo.

With rain falling nonstop, he said there was nowhere left for the water to drain.

“I’m not sure where the water is going because it’s just so much that we can’t really absorb more in the ground at this point,” Acevedo told MSNBC.

The rising water forced a mass evacuation of parts of the city Sunday, and rescuers could not keep up with constant calls for help.

The Red Cross quickly set up Houston’s George R. Brown Convention Center and other buildings as shelters. The convention center, which was also used as a shelter for Hurricane Katrina refugees in 2005, can hold roughly 5,000 people. By Monday morning, it had reached half its capacity, the Red Cross said.

Shardea Harrison checks on her 3-week-old baby, Sarai, who is held by Dean Mize as he and Jason Legnon used his airboat to rescue them Monday from their flooded home. (Joe Raedle/Getty Images)

Residents living near the Addicks and Barker reservoirs — which were created to prevent flooding in downtown Houston — were warned Sunday that a controlled release would cause additional street flooding that could spill into homes. The rising water and ongoing rain put pressure on the dams, which could allow water to spill outside them if the pressure is not relieved.

The Army Corps of Engineers started the reservoir releases before 2 a.m. Monday — ahead of schedule — because water levels were increasing at a rate of more than 6 inches per hour, Corps spokesman Jay Townsend said.

In the Cypress Forest Estates neighborhood in northern Harris County, people called for help from inside their homes as water from a nearby creek climbed to the lower part of their roofs. A steady procession of rescue boats floated into the area.

Angelina De Los Santos, 7, left, Vanessa Pasillas, 2, center, and Jade De Los Santos, 5, center right, watch videos with Rosemarie Pasillas, right, at the George R. Brown Convention Center in Houston on Monday. Thousands of people gathered at the convention center after fleeing their homes. (Jabin Botsford/The Washington Post)

One man, Joe Garcia, carried his German shepherd in the chest-deep water before being picked up by a boat. Garcia said he floated out a tub of his belongings, then went back in for the dog.

The Weather Service warned that the flooding will get worse in the days ahead and that the floodwaters will be slow to recede once Harvey moves on.

Up to 20 inches of rain could fall in the coming days, on top of the more than 30 inches some places have seen, Weather Service Director Louis Uccellini said Monday.

Some people used inflatable beach toys, rubber rafts and even air mattresses to get through the water to safety. Others waded while carrying trash bags stuffed with their belongings and small animals in picnic coolers.

Residents had been given conflicting about whether to evacuate. Governor Greg Abbott urged people to flee from Harvey’s path, but the Houston mayor told everyone to stay home.

The governor refused to point fingers Sunday.

“Now is not the time to second-guess the decisions that were made,” Abbott said at a news conference. “What’s important is that everybody work together to ensure that we are going to, first, save lives and, second, help people across the state rebuild.”

Houston Mayor Sylvester Turner defended his decision, citing the risk of sending the city’s 2.3 million inhabitants onto the highways at the same time.

“If you think the situation right now is bad, and you give an order to evacuate, you are creating a nightmare,” Turner said.