The pledge came after some 200 migrants were sent back to Italy by French authorities over the weekend after they managed to swim across the border.
Clashes between Italian police and the local unit of the European-wide activist group, No Borders, also resulted in one of the officers dying of a heart attack on Saturday.
Police used tear gas to keep the migrants back, and officers arrested several members of the group for alleged possession of weapons.
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.
No Borders had planned to hold another demonstration on Sunday but called it off due to the policeman’s death.
The group has complained that the Italian government's latest efforts to help the migrants were not enough, after a temporary shelter was set up for just 360 people.
But Alfano argued that the fact that, to date, Ventimiglia had not become another Calais – the northern French town where thousands of migrants are camped – was because of stringent railway checks and efforts to reduce the flow of migrants by transferring them to other centres.
Alfano also denounced the activist group, saying its only aim was to exploit the migrant crisis for political gain.
“There will be no leniency towards those who exploit the migrant crisis,” he added.
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.