The Senate will take up a House-passed disaster relief funding package without adding more money after President Trump and his budget director, Mick Mulvaney, promised to send a new funding request for additional aid next month.

Majority Whip John Cornyn, R-Texas, said Senate lawmakers could vote as early as late Thursday or Friday morning on the $36.5 billion supplemental spending package, which House lawmakers passed last week to aid the recovery efforts in states and territories ravaged by three hurricanes, as well as western states burned by devastating wildfires.

Cornyn and Senators from Florida and California staged a last-minute push this week to add more money to the House-passed bill that could be dedicated to helping their states rebuild, but have decided to hold off until a new request is sent next month, Cornyn said.

"I talked to the president and Mick Mulvaney and they promised me there would be another supplemental request coming over mid-November that would include Texas-specific hurricane relief," Cornyn told the Washington Examiner.

Texas sustained more than $100 billion in damages from Hurricane Harvey, which churned over the state for days, causing catastrophic flooding. Texas lawmakers have requested more than $18 billion in federal aid.

For now they are willing to wait and pass the House measure, which will be the second disaster aid package passed by Congress in a little more than a month.

Lawmakers cleared a $15.3 billion package on Sept. 7. Much of the money in both the first and second supplemental measures is allocated to the Federal Emergency Management Agency disaster relief fund and the nation's insolvent flood insurance program, rather than to the states and territories for rebuilding efforts.

"My concern had been every one of these supplementals goes by without addressing adequately the unmet needs of these states, including mine, and that we were missing an opportunity," Cornyn said. "I took the president's commitment as reassurance that they were going to make sure those needs were met not only in Texas but Florida, Puerto Rico, the Virgin Islands and we've also been working with some of the folks out west who have had the wildfire damage. So, we've got a pretty good coalition together."

None of the funding approved so far is offset with cuts or revenue increases, which means it will add to the annual budget deficit and the total national debt.

The latest measure includes a $4.9 billion loan to the nearly insolvent Puerto Rico government will likely never be repaid, lawmakers acknowledge.

Puerto Rico was flattened by Hurricanes Irma and Maria and most of the island remains without power or clean drinking water.