The president and first lady Melania Trump arrived around 1 p.m. in Corpus Christi -- about 40 miles from where the Harvey made landfall as a Category 4 storm late Friday and 220 miles from Houston, which has been inundated with more than 2 feet of rainfall over more than three days. In some locations more than 4 feet of rain was measured.
"We want to do it better than ever before," Trump said at a fire station. "We want to be looked at in five years or 10 years from now as this is the way to do it."
He added the flooding was of "epic proportion."
On Tuesday, a levee breached for the first time and thousands of people have been rescued in boats and helicopters. The area is also bracing for more rainfall before the storm, which has been downgraded to a tropical storm, leaves the region.
Trump, wearing a white USA baseball cap, was briefed by Texas Gov. Greg Abbott and Federal Emergency Management Agency administrator Brock Long. The contingent, which then traveled aboard Air Force One to Austin, the state capital, also included Health and Human Services Secretary Tom Price, acting Department of Homeland Security Secretary Elaine Duke, Housing and Urban Development Secretary Ben Carson and Small Business Administrator Linda McMahon.
After meeting with officials at the briefing, he addressed a crowd gathered outside the firehouse, some of whom displayed signs that criticized the president.
"What a crowd, what a turnout," said Trump, who held up a Texas flag.
Trump, stepping on a low stool and spoke into a microphone, said "thank you everybody."
Abbott earlier greeted the president after his plane landed in Corpus Christi.
"We want him to see and understand the enormous challenges that Texans have faced and the need for the aid that he's providing," Abbott told reporters.
During the appearance at the firehouse, Trump praised the efforts from officials, but turning to Abbott, he said: "We won't say congratulations. We don't wanna do that ... we'll congratulate each other when it's all finished."
In 2005, days after Hurricane Katrina in New Orleans, President George W. Bush notably said to FEMA Administrator Micael Brown: "Brownie, you're doing a heck of a job." Brown was replaced within weeks for his role in the federal response.
Long assured the public that the George R. Brown Convention Center in downtown Houston that is serving as a "mega-shelter" with more than 9,000 evacuees is not like the situation in New Orleans for evacuees.
"This is not the Superdome," Long said of the home of the NFL's Saints. New Orleans' convention center also had deplorable conditions in 2005.
The president's visit follows days of rain and flooding in eastern Texas near the Gulf Coast brought on by Harvey, the hurricane-turned-tropical-storm that continues to hover over the region.
The situation worsened in south Houston on Tuesday, when the levee at Columbia Lakes breached for the first time in its history.
"Get out now!" Brazoria County, where a mandatory evacuation was enacted on Sunday, wrote on Twitter.
"That area is under mandatory evacuation," county spokeswoman Sharon Trower said. "We have some residents there who didn't want to leave. We have first responders there getting them out now."
Several people have died since Saturday due to the severe storm and many others have been injured. By Tuesday, though, the death toll remained below a dozen.
The Houston Chronicle reported Tuesday that a police officer drowned in his patrol car while driving to work downtown Sunday morning.
In addition, six members of a Houston family, including four children, are feared dead. Their van reportedly was swept away by a current while trying to flee rising floodwaters over the weekend.
Houston Fire Department Chief Samuel Peña said his agency has deployed boats and high-water vehicles to help in rescue efforts, and noted that the most afflicted parts of Houston are on the west side of the city. Houston police urged residents to remain in safe locations and not travel unless it is an emergency.
Officials have also urged residents in southeast Texas to boil water as a precaution, in case drinking water becomes scarce.
Between 20 percent and 30 percent of Harris County's 1,777 square miles was underwater Tuesday afternoon, meteorology Jeff Lindner told the Houston Chronicle. Harris County includes Houston, the fourth largest city in the nation.
The greatest rainfall was 51.88 inches at Cedar Bayou and FM 1942, east of Houston in Baytown, according to the National Centers for Environmental Prediction. The agency listed 30 locations with more than 30 inches, including George Bush Houston Intercontinental Airport with 31.18 inches. The city's other airport, William Hobby, measured 27.7 inches.
Both airports remain closed until Thursday.
The entire Texas National Guard is involved in rescue and recovery operations -- bringing the total deployment of about 12,000 guardsmen to Corpus Christi, Houston and the surrounding areas.
The City of Houston has appealed to medical professionals, nurses and social workers to help at the George R. Brown Convention Center. Most locations under mandatory or voluntary evacuations are southwest of Houston's city center.
City leaders refuted a rumor that people seeking help must provide valid legal immigration papers to prove residency.
"We will not ask for immigration status or papers from anyone at any shelter. This rumor is FALSE!" the City of Houston said said on Twitter.
Other big Texas cities hundreds of miles away are setting up mega-shelters -- Austin, San Antonio, Dallas and Fort Worth.
Hurricane Harvey made landfall in Texas as a Category 4 storm late Friday night, and was downgraded to a tropical storm hours later. However, the fallout continues to overwhelm the region of 6 million people, which includes 2 million residents in Houston alone.
FEMA's Long said at a news conference Monday that more than 30,000 displaced residents are expected to be sheltered temporarily in the region.
Harvey, still a tropical storm, will move northeast in the coming days toward Louisiana and Mississippi. Forecasters say it will continue to dump heavy rains until at least Thursday.