Lawmakers in the lower house of Congress voted by 419 to three in favor of releasing the funds, which will mostly be channelled to the Federal Emergency Management Agency (FEMA). The Senate is due to hold its own vote in coming days.
The funds will "allow FEMA to continue response and recovery efforts, including life-saving missions, while also ensuring the agency has resources available should another emergency arise," said Republican Rodney Frelinghuysen, head of the House Appropriations Committee.
"We are with you and we will be with you until we are even stronger than before," he added, addressing Texas flood victims.
The "no" votes were from conservative Republicans who wanted to see the expense offset with other budget cuts.
The funds, however, are only a down payment on the total cost of the disaster, which experts say could surpass USD 150 billion.
The US Senate will vote on the measure in the next days, and may link the aid to increasing the ceiling on the national debt.
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