The Warsaw-based agency released the latest figures a day after the UN refugee agency said the EU's new relocation scheme for refugees fleeing conflict and poverty is "not enough" to address the scope of the problem.
"The total number of migrants who crossed the EU's external borders in the first nine months of this year rose to more than 710,000 with the Greek islands on the Aegean continuing to be the most affected by the unprecedented inflow of people," Frontex said in a statement.
Frontex added however that the number of migrant crossings in September fell to 170,000 from 190,000 in August.
Frontex chief Fabrice Leggeri reiterated his call to member states to provide additional border guards to help deal with the unprecedented migrant influx.
"Urgent assistance is needed, especially for Greece and Italy, to help register and identify the new arrivals," he said, as the EU gears up for an October 15-16 summit focused on migration.
The crisis has exposed deep divisions within the 28-nation European Union over how to distribute the new arrivals - many fleeing conflict in Syria, Iraq and Afghanistan - and how to stem the flow.
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