One government official has resigned so far, and the owner of the Cromagnon club, Omar Chabon, has been arrested.
Authorities said more than 700 others were injured in the fire, which is believed to have been triggered when a crowd member attending a rock concert set off a flare that ignited the foam ceiling.
Emergency exits were locked, some padlocked, preventing people from escaping the inferno.
Juan Carlos Lopez, an official in charge of Buenos Aires’ urban security, was the first Argentine official to resign over the fire.
“When you have a tragedy of this magnitude, someone has to take responsibility and step aside,” said Mr Lopez, the city’s secretary for Justice and Urban Security.
Mr Lopez was responsible for overseeing safety at over 200,000 commercial premises across Buenos Aires.
He said the Cromagnon night club in the capital’s Once neighbourhood had been filled above its licensed capacity during the concert by rock group Los Callejeros, with around 2,000 people inside, almost double the legal number.
There has been an enormous public outcry, with around 1,000 people marching from the club to the town hall via the morgue on Saturday to demand punishment for those responsible.
Marchers called on Mayor Anibal Ibarra to resign, and for tougher safety codes for concert halls and clubs.
“We have to ensure this never happens again,” said Jorge Viegas Mendes, whose 18-year-old son Cristian died in the blaze.
Irate residents will later hold a pot-banging protest, demanding a full government investigation into the country’s worst fire in decades.
Around 263 people remain hospitalised, with 117 of them in serious or critical condition.
Most of the victims died from smoke inhalation, and local reports said bodies were found in a pile near one blocked exit.
Survivors described how thick black smoke set off a stampede for the exits as the concert hall filled with fumes, and people struggled to force open emergency exits.
Authorities said the exits were either wired shut or padlocked to prevent people from entering without paying.
“If the emergency exit had been open, so many people would not have died,” said Mayor Ibarra.
Survivors said security had been tight, with club staff searching concertgoers on the door for banned flares.
“They looked in bags, in shoes, even in our hair. They frisked me from head to toe,” said one woman who lost her husband in the fire.
A staff member got on stage and urged the crowd not to set off flares, a common practice during rock concerts.
However witnesses said he was hissed and booed.