On Monday morning, hours after part of a century-old apartment building crumbled onto a downtown street, officials in Davenport, Iowa, said they were not aware of anyone still trapped in the rubble.

That afternoon, as cleaved-off brick from the unsteady structure left the insides of units exposed, the city announced that its Fire Department had turned over control of the site and that recovery work had begun. Demolition, they said, was “expected to commence” the next day.

But by nightfall on Memorial Day, it was clear that Davenport leaders had badly miscalculated: After protesters gathered at the site, rescue crews found a resident inside the building and pulled her to safety.

“The immediate question I know people are asking is, ‘How did she get there? And why wasn’t she found earlier?’” Mayor Mike Matson said Tuesday as officials acknowledged that more people remained missing. “I am totally transparent with you. I do not know. We do not know.”

The partial collapse of the six-story building near the Mississippi River, and the handling of its aftermath, infuriated residents who questioned whether more could have been done to prevent the collapse and who said the city moved far too hastily to declare the rescue operation complete.

Dozens gathered outside the building on Tuesday, some carrying signs with messages like “Save Lives Not Property.” At least five people with ties to the building remained unaccounted for on Tuesday, officials said, including at least two who were believed to have been inside. No deaths had been confirmed.

Like in New York City, where the collapse of a parking garage with unresolved safety violations killed one person earlier this year, and in Surfside, Fla., where the 2021 collapse of a condo building killed 98 people, there had been warnings about problems at 324 Main Street in Davenport, a city of 100,000 residents situated about halfway between Des Moines and Chicago.

In January, Davenport officials said, a complaint about the building led to brick work, though the structure, home to dozens of units and residents, was deemed structurally sound by an outside engineer. Months later, they said, another report led to permits being issued for repairs, which were underway at the time of the collapse.

Aaron Aguilar, who visited the site of the collapse on Monday, said he used to live at 324 Main and had performed maintenance work there. The structure was badly damaged by a severe storm in August 2020, Mr. Aguilar said, and some residents had to evacuate for a time after that. He said the collapse appeared to have taken place in a part of the building near the worst of the storm damage.

“I cried this morning when I found out what happened,” Mr. Aguilar said in an interview, adding that he still knew people who lived there.

Attempts to reach the property owner on Tuesday were not successful. The authorities said an investigation would take place.

Officials in Davenport defended their handling of the collapse on Tuesday, noting that rescue crews rushed to the scene on Sunday and saved several people despite significant personal risk. In the hours that followed, search-and-rescue teams from across Iowa, including trained dogs, had arrived and had found no sign of anyone still buried in the pile.

“Our continuous evaluation of what to do or not to do happened in real time,” Mr. Matson said Tuesday when he was pressed about why the city had announced plans to start demolition when, it turned out, people were still missing.

With demolition plans on hold, the next steps remained uncertain. Structural engineers and rescue crews said the building was perilously unsteady, doomed to fall on its own at some point, and that even making another sweep would be perilous.

“It’s extremely difficult: You can’t run up to a pile of bricks and rocks and just start throwing things off, as much as we want to,” said Jim Morris, an assistant fire chief and the city’s fire marshal. “We want to get everybody out and we want to do it right now.”

Later in the day, rescue workers entered the building and emerged with six cats, two snakes and a lizard whose owners had provided photos and told them where they were located.

The pets all looked to be in good health, said Erika Gunn, the executive director of the local humane society, who waited outside to examine the animals. “We are excited and relieved,” she said.

But there was no immediate news on the status of the missing residents.

Amy Anderson, who said her family member Ryan Hitchcock was among the missing, asked for calm and respect as crews studied the building and prepared to resume searching.

“I plead with our community just to let the city do their job right now,” said Ms. Anderson, who described Mr. Hitchcock’s Christian faith and said he would not want anyone to be injured searching for him. “It is an absolute no-win situation but this is the best plan of attack and we don’t want anyone else hurt.”

Outside the apartment building, Branden Colvin Jr., 18, said he was “still holding out hope” about his father, Branden Colvin Sr., who remained missing.

The elder Mr. Colvin had returned to the building from work around noon Sunday, visited a neighbor and then returned to his unit to take a nap, family members said.

No one had seen him since. His black Honda Accord remained parked outside.