The bodies of 33 people who died in a diving boat fire off the coast of Southern California have been recovered, leaving only one still missing.

The bodies of 13 additional victims were recovered Tuesday from the waters off the coast of Santa Cruz Island, where the 75-foot commercial vessel the Conception went up in flames early Monday morning, Santa Barbara Sheriff's Office Lt. Brian Olmstead said.

On Monday, the remains of 20 people — 11 women and nine men — were found. Crews on Wednesday were searching for one more body in the 65-foot-deep waters.

The Coast Guard on Tuesday called off the rescue search for the 34 victims, saying they were presumed to be dead. The 33 passengers and one crew member were sleeping below deck when the fire broke out before 3:30 a.m. Monday.

The smoldering remains of the dive boat Conception before it sank off the Santa Cruz Island coast. Santa Barbara County Sheriff's Office

It's unclear if the victims woke up and tried to escape the flames, or perished in their sleep, U.S. Coast Guard Capt. Monica Rochester said.

Five crew members, including the captain, were on the third deck of the boat when it erupted into flames, and were able to jump off the boat. They were rescued by a recreational vessel.

The Conception, operated by Truth Aquatics out of Santa Barbara, was on a $665 per person Labor Day weekend diving excursion, according to a Truth Aquatics schedule. It departed Saturday morning and was due back Monday evening.

The vessel was required to be inspected by the Coast Guard annually and was in full compliance with regulatory requirements, Rochester has said.

Inge Courtois, the general manager of Truth Aquatics, said the company's diving operations were postponed until further notice. She said the five crew members who survived had no choice but to jump off the ship or else they would have died.

She said the crew member who died was 26 years old and died “doing what she loved.” She said the woman, who she did not want to name, was originally hired to work in the Truth Aquatics office, but she wanted "badly" to be on the water "so we put her on the boat."

Santa Barbara County Sheriff Bill Brown said Tuesday that investigators were collecting DNA samples from victim's families to identify remains because the bodies had suffered extreme thermal damage.

A message reading in part "I love you Allie" adorns a makeshift memorial for the victims of a scuba diving boat fire, on Sept. 3, 2019, in Santa Barbara, California Frederic J. Brown / AFP - Getty Images

Susana Solano Rosas identified three of her daughters and their father — Evanmichel Solano Quitasol, Nicole Storm Quitasol, Angela Rose Quitasol and Michel Storm Quitasol — as victims of the fire. Her daughters' stepmother, Fernisa Sison, was also on the boat, Rosas said.

Pacific Collegiate School, a charter school in Santa Cruz, said that two of its students were aboard the Conception with one of the student's parents.

The mother of Allie Kurtz, 25, confirmed to NBC News that her daughter was on the trip and is presumed dead. Kurtz loved diving and "was following her dream," her mother said.

Dignity Health, a healthcare company based in California, released a statement Tuesday that said a nurse and two former staff members were on the vessel but did not release their names.

And Heather Sawdon said in a statement that her sister, Kristy Finstad, a marine biologist who co-owned Worldwide Diving Adventures, was among those presumed dead. The description of the Labor Day weekend excursion advertised that Finstad would be aboard the boat with her microscope.

When the search for survivors was called off Tuesday, crews could focus on "why this incident occurred and what we can learn from this tragedy," Rochester said. A team with the National Transportation Safety Board also began investigating Tuesday.