Ninety-six hours after the cargo ship lost contact, the Coast Guard has only found debris from the ship.
There have been reports of survival suits, life boats and life rafts that have been checked for signs of life, Coast Guard Capt. Mark Fedor said at a news conference Monday.
One of the survival suits contained unidentifiable human remains, he said.
"We are still looking for survivors and any signs of life," Fedor said.
The massive search in the Caribbean Sea has yielded a 225-square-mile debris field but no sign of the ship.
The vessel was carrying a crew of 28 Americans and five Polish nationals when it went missing near the Bahamas last week as Hurricane Joaquin, with winds blowing at 130 mph, passed over the archipelago.
El Faro, based in Jacksonville, Florida, was headed to San Juan, Puerto Rico.
At this point, Fedor said, the Coast Guard is no longer looking for the ship. All efforts are on finding survivors.
The search mission began Friday, Fedor said, but the storm and rough sea conditions made it difficult.
Sunday was the first day the searchers had fair search conditions with which to work, he said.
At this point, "for our search planning efforts, we are assuming it sank in the last known position we recorded on Thursday," Fedor said.
The company that owns the 790-foot ship, TOTE Maritime Puerto Rico, released a statement saying a recovered container "appears to be from the El Faro," but according to the Coast Guard, there is no confirmation it or any of the other objects belong to the missing vessel.
Ties to Jacksonville
Phil Greene, the president of TOTE, told CNN affiliate WFOX/WSVN-TV that most of the ship's crew members had ties to the Jacksonville area, but the company has not released any of their names.
Greene said his focus is on their families, whom he says he's been "upfront" with throughout the ordeal.
CNN affiliate WGME-TV in Portland, Maine, said that at least four of the missing Americans, including El Faro's captain, are from Maine, and that two of them graduated from the same high school and college, Maine Maritime Academy.
CNN reached out to the college Sunday night but did not immediately hear back.
Joaquin disrupts routine voyage
El Faro set out Tuesday on what should have been a routine voyage from Jacksonville to Puerto Rico.
But Joaquin soon barreled into the area, growing in strength.
Family members told WFOX/WSVN they questioned why the ship sailed into what was then a tropical storm, but Greene, the TOTE president, told the station that the boat's captain felt the conditions were favorable and "was very confident the ship was doing well, the crew was quite up to date."
The mother of one of the missing crew members told WGME that she did not blame the captain.
"The blame that has to be done is on the hurricane, not the captain," she said. "The captain is looking out for his crew."