The draft bill would also ease income tax for some 10 million people who earn between €8,000 and €26,000 a year, reduce the amount of government office space and force local authorities to publish all expenses online.
"This is for a simpler Italy," Renzi told reporters.
Renzi explained the €80 monthly "bonus" for the lowest band of taxpayers would start in May, although experts had also expected some provisions for people who pay no income tax because they earn too little.
Within a total of €2.1 billion in cuts, €400 million would come from the defence ministry including €150 million from adjustment to the order for F35 fighter jets from the United States.
Finance Minister Pier Carlo Padoan said the draft bill heralded a "structural adjustment" for the country that will "put gross domestic product (GDP) into a higher growth level than it has been for the past 20 years".
There would also be a 10-percent reduction on business tax and a limit on the salaries of top public sector managers to €240,000 a year, as well as faster repayment of state debts to the private sector.
The draft bill also plans to cut the number of public utilities run by local authorities from 8,000 to 1,000 units within three years as a way of raising funds.
Renzi said the proposed measures, which still have to go before parliament for approval, would cost €6.9 billion in 2014 and €15 billion in 2015.
Tito Boeri, an economics professor at Bocconi University in Milan said the proposals seemed "ad hoc."
"They seem a bit hurried and temporary, even if the government would like them to be structural," he said.
But he added that the measures did appear to "reflect as far as possible" the promises that Renzi made to voters last month shortly after coming to power.
The centre-left leader, who won a power struggle within his Democratic Party against his predecessor Enrico Letta, has no previous experience in national government and was previously the mayor of Florence.