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He needs to seal a formal coalition deal with the small centre-right NCD party to secure a majority and name his cabinet, but will probably seek a vote of confidence in parliament later this week.
Renzi, who engineered the removal of a party rival from the premiership last week, plans a radical programme to lift Italy out of its most serious economic slump since World War Two. However, he will have to deal with the same unwieldy coalition which he criticised for failing to pass major reforms under its previous leader.
"In this difficult situation, I will bring all the energy and commitment I am capable of," he told reporters after President Giorgio Napolitano gave him the mandate to form the next government.
"The sense of urgency is extraordinarily delicate and important but it's also true that, given the time horizon we have set of a full parliamentary term, we'll need a few days before formally accepting the mandate," he said.
The 39-year-old Renzi had been expected to take over since his rival Enrico Letta was ousted as prime minister at a meeting of their Democratic Party (PD) last week, following growing impatience with the slow pace of economic reforms.
Renzi received the endorsement of former British Prime Minister Tony Blair, the foreign politician with whom he is most often compared, who said he had the "dynamism, creativity and toughness to succeed".
However credit ratings agency Fitch underlined the scale of the challenge, maintaining its negative outlook on Italy and highlighting the risk of more political instability.
The euro zone's third-largest economy is technically no longer in recession since it scraped back into growth in the fourth quarter of 2013. However, it remains profoundly marked by the crisis with a 2 trillion euro ($2.7 trillion) public debt, a crumbling industrial base and millions out of work.
Renzi has promised swift action to create jobs, reduce taxes and cut back the stifling bureaucracy weighing on employers and business, but has offered few specific policy proposals and a promised "Jobs Act" expected last month has been delayed.
He said he expected to lay out full reforms to Italy's electoral law and political institutions by the end of February, to be followed by labour reforms in March, an overhaul of the public administration in April and a tax reform in May.
ECONOMY MINISTRY CHOICE EYED
With the formal steps leading to the formation of a new government underway, attention has focused on Renzi's likely choice as economy minister, a position vital to reassuring Italy's international partners.
Speculation has concentrated on Lucrezia Reichlin, a professor at the London School of Economics who is also in the running to become deputy governor of the Bank of England.
If confirmed, her appointment would continue a series of technocrat finance ministers following Bank of Italy official Fabrizio Saccomanni, the incumbent, and his predecessor Vittorio Grilli, a senior official from the Treasury.
Other possible candidates include Fabrizio Barca, a minister in the technocrat government of Mario Monti which ran Italy from 2011 until last year, and Giampaolo Galli, a PD member of parliament and former Bank of Italy economist with a background in the business association Confindustria.
Renzi, who has dominated the political scene in Italy since his sweeping victory in a PD leadership primary in December, declined to comment on the possible makeup of his cabinet. "Our attention is on content and not other issues," he told reporters before returning to his home city of Florence, where he is expected to resign from his current post as mayor.
One area which European Union partners will be watching closely is budget policy, an area where Letta stuck to strict Brussels orthodoxy, squeezing the deficit within the 3 percent of GDP ceiling.
Renzi has said that Italy should be allowed to break the borrowing limits in exchange for structural reforms to encourage economic growth, an approach which could cause conflict with EU partners including Germany.
The prime minister-designate received a boost from the victory of the centre-left candidate in a regional election in Sardinia on Sunday, who displaced a centre-right rival in the first concrete test for the PD since Renzi took the leadership.
Financial markets, which nearly sent Italy crashing out of the euro zone little more than two years ago, have reacted favourably to his expected nomination with 10-year bond yields falling to their lowest level in eight years on Monday.