Officials in Davenport, Iowa, say they're carefully assessing whether rescuers can further search a partially collapsed apartment building -- which they say can topple at any moment -- for missing residents before they order the structure demolished.

Five people are unaccounted for after the back portion of the six-story structure collapsed Sunday afternoon, and officials believe two of those missing may still be in the building, Mayor Mike Matson said Tuesday.

On Tuesday afternoon, emergency crews reentered the building and rescued several animals as they searched portions that engineers believed were safe enough to explore -- but they did not detect signs of human survivors, the city said.

Officials are determining whether further searches are possible as the "extremely volatile" wreckage threatens to crumple even further and poses a significant safety risk for crews who may enter, Davenport Fire Marshal Jim Morris said at a news conference Tuesday.

The debris from Sunday's collapse is currently helping to hold the building up, according to Larry Sandhaas, a structural engineer hired by the city.

"You can't run up to a pile of bricks and rocks and just start throwing things off -- as much as we want to," Morris said at Tuesday's news conference, becoming emotional several times as he spoke. "It's not that we don't want to do this. It's the fact that we have to do it in a safe manner. ... We're going to reevaluate how safe we can be in order to get in there and not currently make the situation any worse."

On Monday afternoon, the city indicated in an online post that demolition was expected to start Tuesday morning, with an official later adding a demolition was necessary "to maintain as much safety for the surrounding area as possible."

A ninth survivor ended up being rescued from the site that day, the mayor said. And by Tuesday morning, the city government posted that the timing of the property's "physical demolition is still being evaluated," though initial phases of the process, such as permitting and staging of equipment, would begin Tuesday.

News that the city was weighing the building's demolition drew protesters this week to the property -- demonstrators who were concerned some residents could still be trapped, CNN affiliate Quad-City Times reported. Some held signs reading, "Who is in the rubble?" and "Find them first!!"

Besides the nine rescued, more than a dozen others were escorted from the site following the collapse, officials said. The cause of the collapse has not been determined.

Rescue and recovery crews have performed multiple searches of the structure using dogs, drones, thermal imaging, infrared and trained rescuers, but found no additional signs of life, Davenport Fire Chief Mike Carlsten said.

All of the building's residents have been displaced, with city officials saying they will not be allowed back into the building to collect their belongings.