As grieving relatives identified their loved ones and the first body was sent home, a harrowing recording emerged of the pilot's final minutes seeking to land the plane without fuel.
Bolivia said it had suspended the charter company LAMIA's permit and ordered an investigation into its operations.
It also suspended the executive staff of the civil aviation authority and the airports administrator for the duration of the probe.
Investigators are examining pilot error and air traffic control problems as possible factors in Monday night's crash.
The disaster killed most of the Brazilian football club Chapecoense Real and 20 journalists travelling with them to a major regional championship match.
LAMIA, which specializes in flying Latin American football teams, has ferried local clubs and national sides around the region, with players including superstar Lionel Messi.
Investigators are trying to piece together the last moments of the doomed flight, which slammed into the mountains outside Medellin with 77 people on board, six of whom miraculously survived.
Forensic authorities who identified the bodies said in a statement Thursday that the dead included 64 Brazilians, five Bolivians, a Venezuelan and a Paraguayan.
The body of the last was scheduled to be flown back to Paraguay on Thursday evening, with the rest departing on Friday, it said.
People participate in a tribute to the players of Brazilian team Chapecoense killed in a plane crash in the Colombian mountains
Details of the jet's terrifying end emerged in an audio recording aired by Colombian media in which the pilot radios frantically that he is out of fuel.
In the recording, pilot Miguel Quiroga contacts the control tower seeking priority to land.
The operator tells him he will have to wait seven minutes for another plane to land first.
"We have a fuel emergency, ma'am, that's why I am asking you for it at once," the pilot replies.
Although the timeline was not immediately clear, shortly after, the pilot radios: "Ma'am, Lima-Mike-India 2933 is in total failure, total electrical failure, without fuel."
The air traffic controller said she had since received threats, blaming people "ignorant" of safety regulations.
There were 72 passengers and nine crew on board the LAMIA plane when it crashed in Colombia
"I can say with absolute certainty that for my part, I did everything humanly possible and technically required to keep those (people) alive," she said in a statement.
Colombia's civil aeronautics agency said the time sequence of the tape was "inexact," and had no comment on the content of the recording.
But the agency's air safety chief, Freddy Bonilla, confirmed that the plane was out of fuel at the moment of impact.
The plane had disregarded international rules on fuel reserves, he said.
Investigators said it would take at least six months to analyze the plane's black box recorders and reach a conclusion.
At the San Vicente funeral home, victims' families gathered in mourning.
Roberto Di Marche, a cousin of late Chapecoense director Nilson Folle Junior, arrived in the team's jersey, then removed it and left it by his cousin's body.
"He was like a son, a brother to me," he said, his voice trembling. "And now he's like this, in a coffin. It's terrible."
The Cinderella-story club Chapecoense had been travelling to what would have been the biggest match in its history, the finals of South America's second-largest club tournament, the Copa Sudamericana.
Tearful tributes were held Wednesday evening, at the time the match was to have been played, in Medellin and the team's hometown, Chapeco in southern Brazil.
Chapecoense media spokesman Andrei Copetti said a big wake was planned in the club stadium for when the bodies were brought home.
In Europe, a minute's silence for Chapecoense will be held before every Champions League and Europa League game next week, UEFA said.
Among the survivors, Chapecoense defender Alan Ruschel was in critical but stable condition in intensive care after back surgery.
Journalist Rafael Henzel and player Helio Neto were listed as stable. Two crew members were likely to leave the hospital Thursday, an official said.
Goalkeeper Jakson Follmann was set to undergo surgery again after having his right leg amputated.