The move, which will only apply to those whose pensions are less than €3,000 a month, is expected to be approved by the cabinet on Monday, La Repubblica reported.
Renzi said the the money will come from €2 billion which has been set aside to fund “measures against poverty”.
Earlier this month, the constitutional court overturned a key plank of the debt-laden country's pension reforms in a ruling that required it to reimburse the money.
In December 2011, when Italy was under severe market pressure over its public debt, the technocrat government in power at the time pushed through draconian austerity measures.
Among the reforms was a hike in the number of years of pension contributions, a change in the calculation of pensions to take into account salaries received through an entire working life rather than the most recent wages, as well as a halt in inflation-adjusted increases for pensions that are above €1,400 a month.
In its ruling, the constitutional court overturned the government's decision to scrap inflation-adjusted pension increases, finding that it is a "constitutionally-founded" right which had been "sacrificed in an unreasonable manner".