The law, adopted last year by the centre-left government that was booted out of power in March, made it compulsory for children in pre-school education to be vaccinated against 10 diseases, including measles, tetanus and poliomyelitis.
Parents who have not vaccinated their children by the time they reach school age (six years old in Italy) face a fine of up to 500 euros.
The new administration -- formed of the anti-establishment Five Star Movement and the nationalist League -- is leading the charge against the law.
Last week, the upper house Senate approved an amendment proposed by Five Star and the League pushing back enforcement of compulsory vaccination for pre-schoolers to the 2019-20 school year, pending a complete revision of the law after the summer recess.
New health minister Giulia Grillo, from Five Star, has drafted a new bill introducing what she calls a "flexible obligation", giving priority to education on the benefits of vaccines, encourages use of compulsory vaccination only over short periods and instances when the coverage rate is too low.
Grillo, a doctor, claims there will be guarantees that children who haven't been immunised could be enrolled in classes where the WHO recommended coverage is assured.
However she also caused outrage when, in an interview with major daily Corriere Della Sera on Wednesday, she said that it wasn't realistic to "make people believe that no one will die" of measles.
Parents currently have to present pre-school institutions with booklets that list the vaccines, updated by the doctors who administer them.
For the 2019-20 school year plans were in place for educators to get vaccine information on each child directly from local health authorities, a measure designed to bypass the possibility of anti-vax parents falsifying documentation.
That measure was adopted in order to fight back against a drop in the number of people being vaccinated that had taken coverage below the 95 percent limit recommended by the World Health Organization (WHO).
That coverage ratio is the minimum required to create the communal immunity that staves off diseases and protects people with compromised immune systems who can't be vaccinated.
Coverage rates increased in Italy following the enaction of the previous government's law, but many regions remain well below the WHO threshold for a number of illnesses.
Data from Italy's National Health Institute released in July showed that four people -- including a 10-month-old baby -- had died from measles between January and May, the same number that died in the whole of 2017. In total over 1,700 people had contracted the disease, while last year 5,400 cases were recorded.
The WHO says that Italy accounted for nearly a quarter of the 21,315 measles cases recorded across Europe last year, when cases of the disease soared across the continent.
The number of cases in Italy alone last year was close to the entire European total for 2016, a record low of 5,273, according to the WHO.
While both Five Star head Luigi Di Maio and League leader Matteo Salvini say they are in favour of vaccines and have vaccinated their own children, they consider the current law "coercive" and criticise it for blocking children's access to education.
Some people are fighting back against the government, with a petition created by concerned parents against the amendment attracting around 100,000 signatures in just a few days.
Several regional presidents have announced that they intend to enforce the vaccine obligation even if it is withdrawn, while the national association of headteachers has also said that the current law would remain in force and that parents would have to present a medical certificate proving their children have been vaccinated.