Senate Majority Leader Mitch McConnell late Thursday set up a vote early next week to pass a $36.5 billion disaster relief funding package, after President Trump urged the Senate not to add more money to the measure and get it approved quickly.

The Senate advanced the bill after a coalition of senators from hurricane and fire-ravaged states agreed to back down on their demands for additional money to be added to the package. President Trump and his budget director, Mick Mulvaney, phoned Senate Majority Whip John Cornyn, R-Texas, on Thursday and promised to instead send a new funding request for additional aid next month.

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, while Florida lawmakers are seeking $27 billion to help recover from Hurricane Irma.

Sen. Bill Nelson, D-Fla., in statement protested "the president's efforts to block any attempt... to add additional money" for Florida, which Nelson said is needed to help Florida's citrus growers whose crops were damaged by Irma.

Nelson placed a procedural hold Russell Vought, Trump's nominee to serve as Deputy Director of the Office of Management and Budget. The hold slows the confirmation process, but does not block it.

Nelson said he made the move, "to make sure we get this money, as promised."

The disaster aid package set to pass next week will be the second Congress has send to the president in just over a month. Lawmakers approved a $15.3 billion package on Sept. 7 following Hurricane Harvey.

Much of the money in both 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.

Trump met at the White House with Puerto Rico Governor Ricardo Rosselló on Thursday to discuss more aid for the U.S. territory. Puerto Rico was flattened by Hurricanes Irma and Maria in September, and most of the island remains without power or clean drinking water.

The package passed by Congress includes $4.9 billion loan specifically to provide the government with the liquidity needed to operate. That loan to the nearly insolvent Puerto Rico government will likely never be repaid, lawmakers acknowledge.

Sen. Bob Menendez, D-N.J., said late Thursday that the bill does not provide enough money for Puerto Rico and he protested a provision giving federal officials control over how the loan money is spent.

Menendez called the bill "both inadequate in scope and unfair in treatment."