A $13 billion package written by Republican senators failed to garner enough votes in the Senate this month, after Senate Democrats, who have been pushing for a major expansion of relief aid for Puerto Rico, argued that it was not enough. The Republican measures have not contained additional aid for Puerto Rico that has been allocated in the House measures.

Democrats have framed themselves as advocates for the island, which as a United States territory does not have voting representation in Congress.

“We should not be picking and choosing who gets disaster relief,” Senator Chuck Schumer of New York, the minority leader, said in a floor speech on Thursday. “When Americans suffer, we all step in.”

Republicans have agreed to allocate about $600 million for food assistance to Puerto Rico. But Mr. Trump has balked at spending any more than that — telling Senate Republicans late last month that “we could buy Puerto Rico four times over” with the federal money already spent on disaster relief for the island since Hurricanes Maria and Irma struck in 2017, according to several people in the room.

The party’s rank-and-file members are more flexible. Senator Joni Ernst, Republican of Iowa, one of the states hardest hit by spring flooding, said Senate Republicans were not averse to sending Puerto Rico more aid. But she suggested that other Republicans, especially Mr. Trump, needed proof that previous allocations had not been wasted.

“Puerto Rico has received dollars for disaster funding; Iowa, Nebraska and all those other states haven’t seen a lick of that, and the Midwest needs immediate relief,” Ms. Ernst said on Wednesday.

Puerto Rican officials say that the island, which suffered a catastrophic blow to its electric grid and housing infrastructure, has been slower to recover, in part, because it is isolated from the mainland — and that billions more in federal aid is needed. According to the Office of Management and Budget, FEMA and other federal agencies have so far distributed $11.2 billion in aid to the island.