The Commission said the funds will help migrants and refugees "facing a humanitarian disaster" by financing warm clothing, blankets, food, healthcare and mental health and psychological support.
The teenagers and students were found dead on Friday after what is believed to have been a New Year's Eve celebration.
Residents have watched the infrastructure around them crumble while local political and ethnic forces quarrel over who gets to run the city.
The Dayton Agreement was a peace deal signed 25 years ago to end the 1992-1995 Bosnian War.
After meeting with members of the country’s tripartite presidency, the EU's top diplomat said Bosnia’s "future is European" but that in order to get there "authorities must step up their efforts to deliver on the reform priorities."
A spat between the city's two ethno-nationalist parties - one Croat, one Bosniak - has created a political stalemate since 2008. The city's residents are paying the price.