"You're going to see very rapid action from Congress -- certainly from the President," Trump said.
Trump said he has "spoken to Congress" and said he believes funding for relief efforts will be approved "very, very quickly."
"We think Congress will feel very much the way I feel and in very much a bipartisan way," Trump said.
Trump also signaled the disaster funding would be addressed separately from a broader budget deal.
Pressed on whether this changed his view on the possibility of a government shutdown, which he hinted at last week, Trump said he thinks "it has nothing to do with it."
"I think this is separate," Trump said.
Congress returns next week with a new item added to an already large to-do list -- providing federal resources to those in Texas dealing with devastating flooding and damage caused by Hurricane Harvey.
There is currently about $3.3 billion left out of the roughly $7 billion Congress approved for the Federal Emergency Management Administration's (FEMA) disaster relief fund for 2017 expenses. Aides from both parties agree the unprecedented storm will require a major relief effort, but say it could take weeks, even months to get a handle on the scope of the disaster and what kind of emergency spending may be needed.
"It is simply too early at this point to determine whether FEMA may need supplemental funding. The FEMA Disaster Relief Fund is funded, as planned, to meet disaster needs this fiscal year. The committee will proceed accordingly should the need arise for supplemental funding after damage and recovery assessments can be made," Chris Gallegos, the Republican spokesperson for the Senate Appropriations Committee, told CNN.
But one senior Democratic aide tells CNN that the costs of helping state and local communities is "likely to surpass" what's currently in the disaster account.
To help stretch its resources, FEMA announced Monday it would invoke what it calls "immediate needs" authority that allows the agency to suspend spending on recovery projects from previous disasters and use the existing disaster relief funds to cover costs associated with Hurricane Harvey.
Trump plans to tour parts of Texas Tuesday
. But with the rain still falling, his administration not yet sent to Capitol Hill a specific request for what is needed for FEMA or other agencies. It's unclear when that might happen.
But as Republican leaders look at legislative heavy lifts this fall -- like funding the government or raising the debt ceiling -- it's possible that those more controversial and internally divisive items could be paired with a disaster relief package, which traditionally receives bipartisan support. Combining the must-pass storm recovery package with a spending bill or legislation to avoid a default could upset members who may not want to vote against helping those in need.
Texas Republican Rep. Pete Sessions said Monday on CNN that there will be a need for Congress to act on resources but also to help get senior government executives in place to coordinate the response.
"We're going to have to figure out how we're going to provide for these people and what the federal component is. We need to make sure that the administration as well as the United States Senate finishes off the confirmation of every single federal official that could possibly relate to this. The President is going to need his full team now, starting as quickly as possible," Sessions said.
AshLee Strong, spokeswoman for House Speaker Paul Ryan told CNN Monday: "We will help those affected by this terrible disaster. The first step in that process is a formal request for resources from the administration."
Democrats in Congress regularly back bills adding more federal money for emergencies without insisting that any offsets be made to pay for them. But in the past, many conservatives have demanded any new money be paid for with cuts in other programs. When Vice President Mike Pence served in Congress, he advocated for cutting federal spending to help pay for the costs of rebuilding after Hurricane Katrina in 2005.
Over the weekend, New York Republican Rep. Peter King, who tangled with some in his party over aid for Superstorm Sandy in 2013, tweaked those like Texas GOP Sens. John Cornyn and Ted Cruz who opposed that bill.
"Ted Cruz & Texas cohorts voted vs NY/NJ aid after Sandy but I'll vote 4 Harvey aid. NY wont abandon Texas. 1 bad turn doesnt deserve another," he tweeted.
Cruz, in an interview on CNN on Monday, insisted he backed relief for Sandy, but opposed other items he described "pork" in that package.
"Of course, the federal government has a critical role in disaster relief. It has before and should continue to, but you should not have members of congress that are exploiting disasters to fund their pet projects, and so there will be time for all of those debates in Washington," Cruz said.
House Minority Leader Nancy Pelosi urged the GOP to support emergency funding.
"Republicans must be ready to join Democrats in passing a timely relief bill that makes all necessary resources available through emergency spending," she said in a statement Monday.
The unprecedented levels of rain and flooding in Texas is also certainly to result in a surge in claims expected for the national flood insurance program. The current authorization for the program expires at the end of September. The major damage caused by Harvey means that the borrowing limit for the program will likely need to be increased.
The program is deeply in debt and broader reform efforts have been discussed, but have split Republicans along regional lines. If they can't agree on a broader bill Congress is likely to pass some type of short-term extension.
"The most common and costly natural disaster facing our nation is flooding," said Sen. Sherrod Brown, the top Democrat on the Senate banking committee, which handles reauthorization.
"It is too early to determine how hurricane Harvey will impact the timeline of NFIP reauthorization, but it is likely that Congress will pass a short-term extension to ensure the program doesn't lapse," he said.
A number of senators have drafted or introduced bipartisan legislation to reform the program. Senate banking committee chairman, Sen. Mike Crapo and Brown introduced a bill this summer that would extend the program for six years. Republican Sen. John Kennedy of Louisiana and Democratic Sen. Bob Menendez of New Jersey -- both of whom also sit on the banking committee -- introduced a reauthorization bill of their own that also provides a six-year extension and a series of reforms.
Meanwhile, the other Republican senator from Louisiana, Bill Cassidy, paired up with unlikely bedfellow Democratic Sen. Kirsten Gillibrand of New York to propose a 10-year reauthorization and gradual access by private insurers.
Beyond the FEMA disaster relief, congressional aides say more resources could be needed for the Community Development Block Grant program run by the Housing and Urban Development Department to help with emergency needs. Highway and transit infrastructure money may be needed to deal with the many roads and bridges that have been affected.
Pence committed in a radio interview with Houston station KHOU on Monday that federal help would get to those who need it.
"We're very confident that the Congress of the United States is going to be there to provide the resources necessary -- not only that that we already have with regard to rescue efforts, but to make sure that the disaster assistance that already some 22,000 Texans have signed up for is available and is there," he said.
"We actually anticipate that as many as a half a million people in Texas will be eligible for and applying for financial disaster assistance, and we remain very confident that with the reserves and with the support in the Congress, we'll have the resources that we need," he said.
CNN's Rene Marsh contributed to this report.