"This isn't the last aid package," Ryan told reporters in San Juan.
"This is the second in more to come. ... When we get that final analysis, the administration will submit yet again to Congress a request for another aid package to respond to these longer-term problems."
He called the island's plight "first and foremost a humanitarian disaster" and praised the "compassionate, resilient spirit" of its people.
"It makes no sense to put temporary patches on problems that have long term effects," Ryan said. "We do believe that there is a very important, proper role at all levels of government to respond to this now, in the meantime, for the immediate term and over the long haul."
Already, thousands have fled Puerto Rico in the three weeks since Hurricane Maria hit. But for the millions remaining the struggle for life's basic necessities seems never-ending.
Many travel hours in search of food and bottled water, only to find empty shelves at most grocery stores.
"I've never seen this in my life, never in my life," Emma Ramirez told CNN affiliate WAPA.
Fuel shortages made it difficult to deliver food in the first days after the hurricane, forcing many stores to close. They have since reopened, but supplies of food remain low.
The food supply chain has emptied, and "resupplying it (will) take some time," Manuel Reyes, vice president of the Puerto Rico Chamber of Marketing, Industry and Distribution of Food, told the TV station.
So far, Maria has claimed the lives of 45 people in Puerto Rico. That number may climb, as 117 others remain unaccounted for.
The US Environmental Protection Agency has said some desperate Puerto Ricans are trying to break into wells at hazardous waste sites just to get water, even though it's unsafe to drink.
This public health threat won't be fully mitigated, the EPA said, until waterways and infrastructure are repaired and power is restored.
Two people have died of leptospirosis, a disease that spreads when the urine of infected animals gets into drinking water, according to San Juan Mayor Carmen Yulín Cruz.
Four deaths in the storm's aftermath are being investigated as possible cases of leptospirosis, the US territory's public security department said Friday.
Dr. Irwin Redlener, director of the National Center for Disaster Preparedness at Columbia University, believes the death toll could be "orders of magnitude higher."
"The causes of continuing fatalities that can legitimately be attributed to a disaster like Hurricane Maria are not straightforward, but it is essential to look beyond the immediate casualties -- for instance from falling debris or drowning -- to fully appreciate the consequences of this disaster," he said.
"Local officials may well be struggling with procedures and capacity in their efforts to conduct this tragic count, but it is critical that the most accurate information available is utilized on the ground to warn people about ongoing public health threats and to promote additional assistance."
Still no power, no water
Food shortages are among the myriad challenges facing Puerto Rico's 3.4 million residents in Maria's aftermath.
Power outages and a shortage of drinking water have plagued the US commonwealth as well. Many communities remain cut off, with roads blocked and no phone service.
Ninety-one percent of Puerto Ricans were without power Friday, rising from 83% the previous day. The Puerto Rico Electric Power Authority, or PREPA, attributed the increase to a failure in the "central system" without elaborating on what that means. There is no Internet, no way to get cell phones working and limited ways to communicate or get information.
More than 1.2 million people are without potable water. Some people line up daily to fill up buckets with water from tank trucks, while others collect water from mountain streams.
What is the government doing?
Some 19,000 civilian and military personnel are supporting the federal relief mission, according to the Federal Emergency Management Agency.
The Army Corps of Engineers is installing power generators and temporary roofs to damaged structures.
This week, FEMA approved a $70 million assistance package
for the Puerto Rico Aqueduct and Sewer Authority for emergency repairs.
Cruz, the target of President Donald Trump's ire after she complained about the federal response, told CNN on Thursday she doesn't still have all the help she needs but that recovery has improved
"Ever since last week, when a new chain of communication was given to us by Homeland Security, accountability has improved and things are starting to improve," Cruz said. "I can now see the light. Imagine the light at the end of the tunnel. I can't see it yet, but I can imagine it."
Thousands flee to Florida
More than 36,000 Puerto Ricans have arrived in Florida since October 3, the state's Division of Emergency Management said.
Representatives of FEMA and local charities, as well as loved ones, are welcoming evacuees at airports.
The state has set up disaster relief centers to help evacuees get medical attention, shelter, clothing and food.
Authorities have estimated that 100,000 Puerto Ricans will eventually arrive in Florida in the storm's aftermath, Ana Cruz, a coordinator with the Orlando's Hispanic Office of Local Assistance, told CNN affiliate WKMG.
"I know what they're going through. That's why we're here -- to help, to assist and to guide," Cruz said.
High unemployment, along with better job opportunities on the US mainland, already had pushed Puerto Ricans to pick up their bags and move, mainly to Florida and Texas, according to the Pew Research Center.
The island's population declined to 3.4 million last year from 3.8 million in 2004.
Florida schools are already seeing an influx of students from Puerto Rico, CNN affiliate WPLG reported
"They've been quickly adapting to our schools," Miami-Dade County Public Schools Superintendent Alberto Carvalho told WPLG. "We are working to transition the kids into the South Florida community."