Around 3,300 job cuts are planned at the Ilva site in Taranto, Puglia, while some 600 jobs would go at the plant in Genoa, where workers are have also protested.
Ilva was nationalised and placed under special administration in 2015 after the Riva family, which owned it, was accused of failing to prevent toxic emissions from its Taranto plant.
The government quickly opened a tender for the heavily indebted company, which used to produce a third of Italy's steel output.
The Taranto site is at the centre of a huge legal case in which experts cited by prosecutors have charged that 11,550 people have died from toxic emissions in seven years.
An offer of €1.8 billion from the Am Investco consortium, which includes Italy's Marcegaglia and the bank, Intesa Sanpaolo, was accepted in June.
The government also said at the time that ArcelorMittal had pledged to invest a further €2.4 billion in the company.