The controversial law, which got final approval in the Lower House on Wednesday, will enable regions to request more power over how tax revenues collected in their areas are spent.
Opposition parties say it will worsen Italy’s north-south divide as it will favour wealthier regions in the north.
The Senate and Lower House whips of the opposition 5-Star Movement (M5S) have written to Mattarella asking him to consider using his Constitutional powers to return the bill to parliament.
This would allow for fresh deliberation on the proposal before it is promulgated.
The M5S, the centre-left Democratic Party and the other opposition groups have said they are going to collect signatures to hold a referendum on abolishing the law.
ANSA
