Gabrielli made the announcement during a visit to Ventimiglia, a Ligurian town near the French border which has become a migrant bottleneck.
He said “the only way to decompress the situation in Ventimiglia is to take the migrants somewhere else”.
Interior Minister Angelino Alfano vowed on Monday that Ventimiglia “will not be our Calais” - the northern French town where thousands of migrants are camped - following days of tensions over the migrant situation there.
Friday saw chaotic scenes as migrants plunged into the sea by the rocky shoals at the border posting in desperate attempts to get into France.
Some 200 people reportedly managed to swim across the border, but were sent back by France.
Meanwhile, clashes between Italian police and the local unit of the European-wide activist group, No Borders, resulted in one of the officers dying of a heart attack on Saturday.
In a process that got underway on Wednesday, migrants are being taken by bus to Identification and Expulsion centres in southern Italy before being deported, Gabrielli said.
Italy is having similar issues at its borders with Switzerland and Austria.
Some 500 asylum seekers are camped out in the Lombardy city of Como after being turned away at the Swiss border, the Catholic church-run charity, Caritas, said on Monday.
In April, Austria threatened to build a fence at the Brenner crossing point unless Italy stemmed the flow of migrants across the border, prompting protests from activists. The situation there has been calmer in recent months after hundreds of Italian officers were dispatched to guard the crossing.
Over 94,000 migrants have arrived at southern Italian ports so far this year.