Mr. Trump’s political adversaries quickly pounced on what they said was evidence of a lack of interest or urgency on the part of the president. And some saw an echo of the comments made in 2005 by former President George W. Bush, when he praised then-FEMA head Michael Brown for doing “a heck of a job” in the midst of what was widely seen as a slow and botched recovery effort in New Orleans after Hurricane Katrina.

“The problem is, and this is what felled the Bush administration: images tell the whole story,” said Dan Pfeiffer, who served as a communications director and senior adviser for former President Barack Obama. “You had Trump on Twitter saying one thing, and then you have the images all over cable news telling a different story.”

Peter Feaver, a national security official for Mr. Bush during Katrina, said there were many similarities between Hurricane Maria and the 2005 storm, each of which hold lessons for Mr. Trump and his team.

“There are echoes to it that should concern the White House,” Mr. Feaver said. “They would be wise that they not take it for granted that they can avoid that image stamped on this episode.”

“What matters more is the perception than the reality,” Mr. Feaver added. “The best after-action histories did not condemn Bush as vividly as the immediate media framing.”

The administration is unquestionably facing a daunting task. The hurricane knocked out nearly all of Puerto Rico’s electrical grid, and most of its cellular service. Roads are damaged, bridges have collapsed, and an unknown number of Puerto Ricans are stranded in the hills and hollows of the mountain interior without access to water or food.

Representatives of the commonwealth government stationed outside the capital have taken to driving to San Juan in person to present their progress reports. On Friday, Gov. Ricardo A. Rosselló said that the government would begin commandeering and giving away at least 3,000 containers of cargo stuck at the Port of San Juan, much of it meant for the island’s supermarkets, if the stores themselves could not move the merchandise.