Warning that the influx of migrants has probably not yet "reached its peak", Fabrice Leggeri called for European states to detain unsuccessful asylum seekers so they can be "rapidly" sent back to their countries of origin.
"EU states must prepare for the fact that we still have a very difficult situation ahead of us in the coming months," added Leggeri.
Last month, Frontex said that 710,000 migrants had entered the EU in the first nine months of the year but cautioned that many people had been counted twice.
"This means that a large number of the people who were counted when they arrived in Greece were again counted when entering the EU for the second time through Hungary or Croatia," explained the agency.
Also Read
According to the most recent figures from the UN refugee agency, more than 744,000 people have made the perilous journey across the Mediterranean this year, the majority to Greece.
Today, the first set of 30 migrants was due to leave Athens for Luxembourg under an EU plan to redistribute people throughout the 28-member bloc in order to ease pressure on countries like Greece and Italy.