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Harvey's onslaught is predicted to continue for the next few days, as the storm swirls around the southeastern U.S. coast, briefly heads offshore and then makes another landfall.

The president has been monitoring the storm for days, tweeting frequently about the historic rainfall, rescue operations, coordination between government agencies and volunteer efforts.

"We want to do it better than ever before", he said.

"We will just have to watch". City officials were preparing to shelter up to 19,000 people, with thousands more expected to flee the area as the flooding entered its fourth day.

President Trump will survey the ongoing damage in Corpus Christi and Austin, Texas on Tuesday, after he said he believes Congress will act swiftly to provide funding to affected areas.

Much of the Houston area remained underwater on Tuesday, and unsafe rescues went on through the night as police, firefighters and National Guard troops in helicopters, boats and trucks pulled stranded residents from flooded homes.

Matt Sebesta, the chief administrator of Brazoria County, urged residents on Tuesday of the Columbia Lakes neighbourhood to leave. The driver reportedly called out to them to try to get out through the back door, but they were unable to escape. "We have uncertainty in how the water is going to react", when releases from the reservoirs hit overflowing drainage.

Houston is getting a bit of a break from the relentless rain.

All over Houston, you see what's being called the Texas Navy: private citizens pulling their fishing boats behind pickups.

The official death toll from the storm stood at three, although three others were possibly linked to the massive storm.

Houston police chief Art Acevedo said he was anxious the death toll could climb once the rains stop, waters recede and recovery efforts begin.

"He said he would so I'm sure he's going to".

Harvey is expected to produce 10 to 20 additional inches (25 to 51 centimeters) or rain over the upper Texas coast and southwestern Louisiana through Thursday.

Most of Harvey is predicted to pass into southeast Arkansas on Thursday night and curve into northern MS on Friday morning, forecasters said early Tuesday.

The storm center was in the Gulf of Mexico about 115 miles (185 km) southeast of Houston on Monday morning.

Hawaii has logged isolated reports of greater amounts at high elevations from tropical systems, but the footprint from Harvey in Southeast Texas is much larger. The Governor of Texas, Greg Abbott, has increased National Guard numbers to 12,000, the maximum number possible.

"While my heart is heavy looking at the images of stranded families and damaged neighborhoods, I'm in awe of the bravery of first responders and civilians who are out there rescuing and supporting their neighbors", Wolf said.

Trump already has declared 18 counties in Texas and Louisiana as disaster areas, making them eligible for federal help.