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More than 300,000 people have asked for disaster aid, Mr Pence said
The White House will ask Congress for emergency funding to help those affected by Hurricane Harvey.
“The American people are with you,” Vice-President Mike Pence said during a visit to Texas.
“We will be here every day until this city and this state and this region rebuild bigger and better than ever before,” he said.
President Trump is expected to propose an initial $5.9bn (£4.56bn) in aid, the Associated Press news agency reports.
Texas Governor Greg Abbott said earlier the state might need more than $125bn from the federal government.
At least 39 people have died in the storm and its aftermath.
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Mr Pence said 311,000 people had registered for disaster assistance, and that he hoped for bipartisan support in Congress for the funding request.
It is not yet clear how quickly funds might reach victims.
Visiting the battered town of Rockport, Mr Pence paid tribute to the people of Texas: “The sights and sounds and conversations we had today were just overwhelming.
“I think the resilience of the people of Texas has been inspiring. To see people who’ve gone through the horror of one of the largest natural disasters in American history to be standing shoulder to shoulder, passing out food to their neighbours, helping their neighbours clear out their homes with a smile on their face… it’s humbling to me and it’s deeply inspiring.”
The White House also said Mr Trump would donate $1m of his own money to the relief effort.
As floodwaters recede, the focus has turned from rescue efforts to long-term recovery but residents are being warned not to return home until they are told it is safe to do so.
Earlier, a senior White House aide said about 100,000 homes, not all of which were fully insured, had been affected by the storm and the flooding that accompanied it.
About 779,000 Texans were ordered to evacuate, and another 980,000 left their homes voluntarily, Reuters news agency quoted Department of Homeland Security Acting Secretary Elaine Duke as saying.
The US Federal Emergency Management Agency (Fema) said its teams had rescued more than 3,800 survivors, and more than 90,000 people had already been approved for disaster assistance.
Fema also warned that residents were being targeted by scams. There are reports of individuals impersonating inspectors and immigration officials.
Others were receiving scam calls about flood insurance claiming a premium must be paid or the insurance would be lost.
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Energy suppliers in the south of Texas were forced to shut down refineries and close off pipelines, sending petrol prices higher across the US. Many have now begun the process of restarting their operations, but it could take weeks before production is back to normal.
BBC