A restive region struggles with a fading EU, the arrival of the Trump administration, and the rise of Russia.
Foreign ministers extended the invitation to begin "accession talks" to Montenegro at a meeting in Brussels Wednesday.
Since Hungary closed its borders on Friday, nearly 20,000 people have crossed into tiny Slovenia.
An estimated 8,000 Bosniak men and boys were slaughtered in the Srebrenica massacre.
Severe flooding has prompted the evacuation of tens of thousands of people and left dozens dead. The number of people impacted by the high water is expected to be much larger.
Parts of Bosnia and Serbia have declared a state of emergency.