Deputy Premier and Transport Minister Matteo Salvini's League party on Thursday with drafted a proposal that would have removed the limit on the mayors of towns and cities with more than 15,000 inhabitants serving no more than two terms.
But Salvini said the League was pressing ahead with its bid to remove the two-term limit for regional governors.
The issue has reportedly caused tension within Premier GiorgiaMeloni's ruling coalition.
Meloni's right-wing Brothers of Italy (FDI) and the other main alliance partner, the centre-right Forza Italia of ForeignMinister Antonio Tajani, have both said they are against scrapping the two-term limit.
Several governors face having to step down the next time their regions hold elections unless the limit is removed.
These include the League's popular Veneto Govenor Luca Zaia.
Zaia has been in charge of the region since 2010 and is already on this third term.
He was able to stand again in 2020 because Veneto did not incorporate the national law setting the two-term limit into its regional election law until 2012.
This meant that, given as the measure cannot be applied retroactively, Zaia's first term did not count in this regard.
Meloni is reported to be against dropping the two-term limit because she wants more regions in the hands of representatives of her di lei FdI di lei in order to reflect the fact that it has become the driving force of the right / centre-right alliance.
The Senate's constitutional affairs committee, meanwhile, approved a proposal to allow university students to vote in June's European elections in the cities where they study if that is not their home town.
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