The background is a citizens' initiative by the far right calling for the mass deportation of undocumented immigrants.
The initiative - which critics warn could also be aimed at people with Italian citizenship - has collected 50,000 signatures and will therefore be debated in parliament.
Several thousand people gathered for a demonstration in support, where some made fascist salutes and chanted "Duce!" referring to former dictator Benito Mussolini.
At the same time, tens of thousands gathered for a counter-demonstration organized by various left-wing groups and unions.
A large police force was deployed and no violence has been reported.
The proposal splits Prime Minister Giorgia Meloni's right-wing coalition, with the far-right Lega party expressing support.
