Below the shattered windows of the high-rise hotels in downtown Acapulco, people walk alongside towering hills of garbage bags filled with rotting food and debris, from mattresses to Christmas decorations. Volunteer firefighters from distant states clear the waste, wiping away swarms of cockroaches from their arms.

Miles from the coastal beachside resorts, Elizabeth Del Valle, 43, listened as her teenage daughter Constanza Sotelo, described the “mountains of trash” still blocking many streets surrounding their home.

“We have no way to find face masks to keep ourselves healthy,” said Ms. Del Valle. “We expect that we’re going to get an infection from the smell, from the garbage.”

Weeks after Hurricane Otis shocked forecasters and government officials by intensifying rapidly into the strongest storm to hit Mexico’s Pacific Coast and devastate much of Acapulco, residents say they now face an unfolding public health disaster.

Many locals, public health officials and emergency responders say they believe that the uncollected garbage is linked to stomach infections, diarrhea and skin rashes and other ailments that people have complained about since the storm.

Local business groups this past week called on federal and state officials to declare a sanitary emergency citing “the accumulation of garbage, construction material, lack of potable water and the presence of insects and harmful fauna,” including human remains.

As thousands of troops descended on Acapulco after Otis made landfall, authorities first prioritized clearing debris and restoring power to the tourist resort areas, according to city officials, local business leaders and residents. Some hotels in that area have since reopened.

But people who live outside the city’s beachfront tourist neighborhoods say they must navigate so many piles of trash and debris that in some places it is hard to reach hospitals and health centers.

Even as the authorities respond to Acapulco’s many needs — providing water to residents, restoring power and finding missing people — federal and local officials are sounding alarms over the hurricane’s longer-term health consequences and say that clearing trash needs to be priority.

The city’s mayor estimates that 666,000 tons of garbage are piled across Acapulco. Under normal conditions, local officials said, 700 to 800 tons of waste are picked up every day.

Mexico’s president, Andrés Manuel López Obrador, has promised a quick recovery, saying that families in Acapulco will be “content by Christmas.”

The mayor, Abelina López Rodríguez, believes the timeline will be far longer. “To say that in one month or five months we will rebuild Acapulco would be a lie,” she said.

The president’s support is vital, Ms. López Rodríguez said, “because garbage does not forgive.” The situation could soon become “a health crisis,” she added.

Since Otis ravaged Acapulco — killing at least 50 people and leaving 30 missing — health brigades made up of federal workers have cleaned and disinfected a little more than one-third of the city’s 507 neighborhoods, disposing of hundreds of pounds of rotting food, Mexican officials said.

Natural disasters can often result in an outbreak of infectious diseases, public health experts said. Piles of garbage left outside can attract mosquitoes and rats, which can then spread infectious diseases. A lack of power can also lead to contaminated food, raising the risk of stomach infections and illnesses.

After Hurricane Katrina in 2005, the Centers for Disease Control and Prevention reported skin lesions, diarrhea and pneumonia among evacuees.

Health problems linked to uncollected trash are “more common than we anticipate,” said Amber Mehmood, an associate professor of public health at the University of South Florida who focuses on global health and disaster management. Debris and waste, she said, can become a “breeding ground for mosquitoes that can carry malaria and Zika virus.”

“There are plenty of reasons to be worried,” Ms. Mehmood added.

Leslye Solís Mireles, 31, a firefighter and paramedic leading a team of more than 50 firefighters from another Mexican state, said her crew in Acapulco had helped treat people with various illnesses that she believes stem from the accumulating garbage.

“It is literally a source of infection,” she said, adding that she and many of her own firefighters were now suffering stomach infections and skin rashes.

Ms. López Rodríguez said her government would have to expand the city’s landfill and find more equipment to get rid of the enormous amount of garbage. Acapulco needs 500 trucks to clear the debris; as of now the city has roughly 150 available, she said.

So far, more than 211,000 tons of garbage has been collected, according to the Guerrero state government.

Otis also destroyed 12,500 utility poles in the city, the mayor said, though the electricity commission said on Friday that 89 percent of users in Acapulco have had power restored. But thousands who had their homes severely damaged still lacked electricity, most of them in poor or outer rural neighborhoods, city officials said.

Ms. López Rodríguez is pleading for patience among her frustrated constituents. By the end of the year, she is focused “on having at least our streets clean, our houses clean, to having the water and electricity systems up and running.”

“I appeal to understanding, because a natural phenomenon of such magnitude exceeds any effort that is quick,” Ms. López Rodríguez added. “I don’t want to say that it can’t be done, but it can’t be done from one day to the next.”

W. Craig Fugate, an administrator for the Federal Emergency Management Agency under President Barack Obama, said that clearing debris from the streets was also vital to allow access to vehicles carrying supplies.

Beyond the health threat, Acapulco also needs to ensure that it is ready to welcome tourists, he said. “The last thing I want if I’m able to get anything open,” Mr. Fugate said, “is the smell of rotten garbage in my street. It’s a nuisance, potentially a public health risk, but it’s also an eyesore.”

But some residents in rural areas of Acapulco say they have waited long enough.

On a recent afternoon, Maricruz Balboa rushed down from her hillside neighborhood when she heard that businessmen from another state were giving away supplies from a box truck parked on the side of the street. A crowd of desperate residents reached for soap, hand sanitizer, food and sneakers.

“We’ve had almost no help here so far,” said Ms. Balboa, 48, showing the treasured items she had been given: a couple of water bottles, fruit, vegetables, shampoo and sanitary pads.

Ms. Del Valle made sure to get hand sanitizer from the same truck when it parked near her neighborhood. She said it was the first time someone had come to deliver food and supplies to her community.

“The government is giving as much as it can,” she said. “But it’s not enough.”

There are some signs of a comeback. Various businesses — al pastor restaurants, barber shops and fruit stands — have reopened.

Residents have on their own cleaned debris outside their homes. On a recent Wednesday afternoon, children played with a kite in one area of a grassy field otherwise filled with trash.

“Whether you are a government official or not, whether you have money or not, there is support,” Octaviano Roque Ruiz, 75, a retired teacher, said as he walked out of a tent where government officials were handing out stipends to older people to help them recover from the storm.

Already diagnosed with high blood pressure and diabetes before the storm, Mr. Ruiz said he now had intestinal pain and what appeared to be conjunctivitis. He had tried to go to the hospital recently but was told that it was beyond capacity and to return another day.

Other residents said conditions in Acapulco had made it impossible to live there for now.

Nicolás Linares, 59, left Acapulco briefly after Otis made landfall to join his brother in Zihuatanejo, a coastal resort about 150 miles north, but returned this month after hearing rumors that services had been restored.

“And I arrive and it’s not true,” he said, adding that the room he rents in the city had no electricity or water.

Mr. Linares tried to return to Zihuatanejo on a recent afternoon, but no more tickets were available at the bus station. He said he would return the next day.

“Now I have to go back to my neighborhood,” he said. “I have no other choice.”