"Over the nine and a half months of 2015, the republic’s borders have been illegally crossed by 383,453 migrants," national police deputy spokesman Kristof Gal told the M1 broadcaster.
Gal said police were currently conducting investigations against 741 people.
The Hungarian police online database lists 4,808 illegal border interceptions as of late Thursday. All but a few migrants are known to cross into Hungary from Croatia since the closure of the Hungarian-Serbian border last month.
On Thursday, local media reported that a Hungarian-Croatian border fence had been completed.
According to the EU border agency Frontex, more than 710,000 migrants arrived in the European Union within the first nine months of 2015. Hungary serves as an EU transit country for people fleeing conflict-torn homelands in the Middle East and Africa to seek refuge in Austria, Germany, Sweden and other affluent member states.
