* Renzi to be Italy's youngest-ever prime minister
* Must overcome unease over way he pushed out party rival
* Weak growth underlines economic challenge
* Pledges radical reforms to transform economy
By Gavin Jones and James Mackenzie
ROME, Feb 14 (Reuters) - Matteo Renzi is one step from becoming Italy's youngest-ever prime minister after swiftly dispatching Enrico Letta in a party coup, but the manner of his political triumph could make it harder to carry out the bold reforms needed to resurrect the economy.
After Renzi and the rest of the centre-left Democratic Party (PD) leadership forced Letta to quit by withdrawing their support at a special meeting on Thursday, the prime minister handed his resignation to President Giorgio Napolitano.
Napolitano will hold two days of consultations leading to the appointment of a successor. The 39-year-old Renzi, whose PD is the biggest party in parliament, could be named premier as soon as this weekend.
Ironically, the fall of the government coincided with an implicit recognition by Moody's investor services that Italy's economic outlook had improved during Letta's administration.
Moody's on Friday night lifted Italy's sovereign rating outlook from negative to stable, signalling a possible change in sentiment towards the country's sovereign debt since the start of the euro zone crisis.
Renzi, who would be the third Italian prime minister in a row to be appointed without winning an election, faces intense pressure to achieve the structural reforms that have eluded Italy for years.
Though he has long been agitating for sweeping change in Italian politics and won a landslide victory for his party's leadership in December, few had expected him to snatch power from Letta so soon.
Renzi's decision to bring down the prime minister matured over the past fortnight, according to people close to him, after mounting pressure from unions and Italy's business lobby which have criticized the Letta government for not doing enough to help the country's struggling corporate landscape.
"The change came after a rather abnormal piece of pyrotechnics but I wouldn't waste too much time on the whys and hows of it all. The problem is this: Can he help get the country moving again?" Carlo De Benedetti, one of Italy's most prominent businessmen, said at an event in Turin.
"If he can, the way the change happened will be forgotten. If he can't, that is all that will be remembered," he said.
Renzi has shown himself a decisive, even ruthless political tactician but the structural problems that have made Italy one of the world's slowest growing economies over the past two decades will be a tougher challenge than sidelining rivals.
Data from statistics office ISTAT on Friday showed a 0.1 percent rise in economic output in the final quarter of last year, the first increase since 2011.
The meagre scale of the growth underlines how slowly Italy is emerging from its worst recession since World War Two and how far it has fallen behind other European economies like France or Spain, let alone continental champion Germany.
Over the whole of 2013 the economy, the third largest in the 18-member euro zone, contracted by 1.9 percent after a 2.6 percent drop the year before.
Gross domestic product has shrunk around 7 percent in the last five years and industrial output has fallen by 25 percent. Hundreds of thousands of companies have gone out of business and in the southern half of the country less than half of the working age population has a job.
Italy's 2 trillion euros of public debt are equivalent to more than 130 percent of total economic output and its 12.7 percent unemployment rate is at a level unseen since the 1970s.
"What Italy needs at this point is not a reformer, it's a revolutionary," said one senior official from business lobby Confindustria.
Business leaders have called for quicker reforms, with an attack on stifling bureaucracy and a reduction of the heavy tax burden on employers. Boosted by his sweeping victory in the PD leadership primary last year, Renzi has promised a radical programme but acknowledged that he faces serious risks.
The manner in which he wrested power is likely to weigh heavily on his government, politicians and business people say, and could hamper his ability to overcome the resistance he will inevitably encounter from entrenched lobbies as well as many sceptical members of his own party.
Opinion polls suggest most Italians disapproved of Renzi taking over from Letta without an election, and voters will have an early chance to show their dissent at a ballot to elect the regional government of Sardinia on Sunday.
One party official close to Renzi said some PD members were made uneasy by what they saw as a grab for power.
"The only way he can win them back is by acting, by doing things that transform the country," he said.
It will not be easy. For example, scores of amendments in parliament have already held up the electoral law reform Renzi has proposed to ensure there is no repeat of the unwieldy coalition Letta struggled to lead.
The PD leader will have to cut through the swathes of political and societal resistance that have in the past thwarted Italian reform efforts. And as an outsider with little knowledge of the corridors of power, he might find it even harder than his predecessors.
Already Renzi's forces are likely to have to engage in a period of horse-trading with the small New Centre Right party, whose support the PD needs for its majority in parliament. The party, run by Angelino Alfano, has called for a rightward turn and has ruled out liberal social policies that Renzi has advocated, including gay civil unions.
Italy's soon-to-be prime minister may also find that European Union partners who appreciated Letta's adherence to the bloc's strict budget rules are less impressed by his suggestion that a promise of structural reforms should get Italy room to loosen borrowing limits.
"The structural reform agenda will not go away and the fiscal challenges will not go away," one senior EU official said. "The room for manoeuvre for Italy given its debt level is fairly negligible."