The storm is Trump's first major natural disaster in office and will be the first major hurricane to hit the U.S. since 2005.
"Now is not the time to second-guess the decisions that were made", Abbott said. Fourteen people have also been injured.
Houston's Bush Intercontinental Airport announced it has cancelled all commercial flights today.
The storm hit Texas Friday as a Category 4 hurricane and has slowly moved in a northeast direction since.
Harvey came ashore late Friday as the most powerful hurricane to hit Texas in more than 50 years. "This event is unprecedented & all impacts are unknown & beyond anything experienced", the National Weather Service Tweeted on Sunday morning.
Please, do not use the HFD (Houston Fire Department) social media accounts for rescue request. "We are measuring it not in inches but in feet", Texas Gov. Greg Abbott said on "Face the Nation".
President Trump will travel to Texas on Tuesday, according to White House press secretary Sarah Huckabee Sanders. Then he continued to appreciate, slack-jawed, how much damage Harvey was doing. They have been mobilizing additional resources to move into the areas devastated by Harvey to provide help and comfort as needed.
MARTINEZ: Are you able to get out of your building? "It's pretty horrible right now".
Galveston-based storm surge expert Hal Needham said forecasts indicated that it was "becoming more and more likely that something really bad is going to happen".
Tens of thousands of Texas residents have fled inland to avoid wind and flooding from the threatening storm.
"We're doing absolutely the best we can".
Help pets in need by donating time or money to the San Antonio Humane Society.
Emergency responders completed more than 1,000 high-water rescues during the night.
Mr Trump rolled back the Federal Flood Risk Management Standard set my Barack Obama two weeks ago to ensure new infrastructure wasn't slowed down.
Throughout the country, charities were gathering relief supplies.
The federal government has 5,000 people on site in Texas and Louisiana, where the storm continues to bring torrential rains and flooding.
Houston mayor Sylvester Turner said 40 boats would be added for rescuing people from high waters that have filled neighbourhoods and highways. "This will give us a lot of business in the near future, but you really don't want to see these types of things happen".
The monster storm has claimed 10 lives so far.
"New York City is sending 120 emergency personnel to Texas to assist in the aftermath of Hurricane Harvey", New York Mayor Bill de Blasio wrote on Twitter Sunday.