Local media reported that riot police were called to "isolate" individuals after dozens flooded out of the gates to escape the poor conditions of the centre.
Criticism is mounting about conditions in the home, which housed boys as well as girls.
Its toll updated an earlier count by a police official of "more than 17 bodies of girls" discovered.
Guatemalan media previously reported the centre suffered from overcrowding, with 500 people packed into a space designed for 400.
Grieving relatives held the candlelit vigil outside Guatemala City's National Palace on Wednesday evening to mourn the victims of the blaze, which has so far claimed the livesof at least 35 girls.
President Jimmy Morales said on national television that he had ordered the dismissal of the shelter's director.
The shelter accepted abused, neglected or homeless children as well as those who had completed sentences at juvenile detention centers.
A fire that erupted in a Guatemala shelter for abused teens has killed around 35 young girls and left numerous families demanding justice for their loved ones. Investigators said she was strangled by one of the inmates.
Investigators were trying to determine whether the fire was started by a group that authorities had isolated after the escape attempt on Tuesday night.
Plagued by Latin America's highest rates of child malnutrition and street gangs that often prey on minors, Guatemala has always been a traumatic place to grow up. The conditions have prompted thousands of Central American children from Guatemala, Honduras and El Salvador to flee thousands of miles, often unaccompanied, to the US, producing a crisis at the southern border in 2014 and 2015 that led to the creation of the Central American Minors (CAM) program.
" 'We had 15-19 new arrivals a day, every carer had 34 children to look after, and we were on one day on, one day off shifts of 24 hours because there were not enough staff, ' the employee said, adding she faced death threats and verbal abuse from her wards."
A prosecutor for upholding children's rights, Hilda Morales, told reporters she was seeking to have the shelter closed due to authorities' inability to manage it and the series of complaints.