HOUSTON —  Helicopters plucked desperate flood victims from rooftops Sunday while boats and trucks swept hundreds more residents to safety as the remnants of Hurricane Harvey fueled historic rains and devastating flooding across a wide swath of East Texas.

The unrelenting rain was forecast well into the week, and the Texas Gulf Coast braced for days of catastrophic flooding. The National Weather Service said some areas could be slammed with an "unprecedented" 50 inches of rain by week's end.

"This event is unprecedented & all impacts are unknown & beyond anything experienced," NWS tweeted. "Follow orders from officials to ensure safety."

The storm had claimed at least two lives by early Sunday, but it was too soon to know the full extent of the death and destruction as power and cellphone outages made communications difficult.

"The flooding in and around America's 4th most-populous city is going to write world headlines and set records for generations," tweeted meteorologist Roger Edwards of the National Weather Service Storm Prediction Center.  

President Trump lauded teamwork among the various agencies battling the disaster. 

"I will be going to Texas as soon as that trip can be made without causing disruption," President Trump tweeted Sunday. "The focus must be life and safety."

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Flooding was overwhelming the Houston metropolitan area. The National Weather Service said parts of Harris County had been hit with more than 20 inches of rain in 24 hours.

This is “worse than the worst-case scenario for Houston,” tweeted WeatherBell meteorologist Ryan Maue.

Mayor Sylvester Turner said emergency officials had been overwhelmed with more than 2,000 calls for rescue, and he urged residents not to call unless their situation was life-threatening. He ordered the city's George R. Brown convention center opened as a shelter.

Turner confirmed one death in Houston, saying a woman drowned trying to flee her car in high water. Another death was reported in a house fire in coastal Aransas County.

Turner defended his administration's decision not to call for evacuations ahead of the storm, saying it was too difficult to determine which areas of the sprawling city of more than 2 million people were likely to take the worst hit. The entire city has seen at least some flooding, he added.

“You give the order to evacuate (and) you are creating a nightmare," he said.

Gov. Greg Abbott said more than a thousand state emergency personnel were aiding local authorities in water rescues. The Coast Guard, which said it had received more than 300 requests for search and rescues, had five helicopters conducting rescues in Houston, with more choppers coming in from New Orleans.

"If you are in a flooding situation, stay calm, do not panic," the Coast Guard said in a statement. "Do not go into the attic, rescuers from the air cannot see you."

Officials are urging people to stay off of the roads.

"It's so dangerous that people would give themselves the death penalty," said Houston Police Chief Art Acevedo, who was out with his officers making water rescues in his saturated city Sunday.

"Sad, breaks your heart for our city and our state," Acevedo said. "But it's Texas. We'll get through it."

Lindner called the rainfall totals "staggering." And more torrential rain is coming: Harvey is nearly stationary and little in the way of movement is expected through Monday, the weather service said.

The floodwaters themselves are a hideous, toxic brew, with reports of alligators and swarming fire ants in the water.

In Aransas County southwest of Houston, where the storm made landfall Friday night, Sheriff Bill Mills said 30 to 40 people remained unaccounted for as of Saturday evening. About 30 people were being treated for injuries in his county alone, he said.

Two Aransas County municipalities, Rockport, with a population of 10,000, and Port Aransas, with about 4,000 people, took the brunt of the storm as it slammed into the coast. At least 10 injuries were reported from collapsed roofs in Rockport, which is 25 miles northeast of Corpus Christi and 220 miles southwest of Houston.

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Nearby Port Aransas was particularly vulnerable perched on a narrow strip of Mustang Island, which sits at the entrance to Corpus Christi Bay. It registered the strongest wind gust of 132 mph from Harvey, according to the National Weather Service. 

The two towns, like dozens over others in the area, reported widespread damage as emergency teams searched for any survivors trapped in low-lying areas or collapsed buildings.

Meteorologists were awed by the scope of the disaster.

“This could easily be one of the worst flooding disasters in U.S. history,” tweeted Weather Channel meteorologist Greg Postel, who said he cannot think of an analogous flood event.

Homer reports for KHOU-TV in Texas; Rice and Bacon for USA TODAY in McLean, Va. Contributing: Julie Garcia, Corpus Christi Caller Times; Doug Stanglin, USA TODAY