UPDATE 5-Two policemen shot as new Italy government sworn in
* Italian gunman wanted to shoot politicians
* Police officer shot in neck, seriously wounded
* Centre-right gives Letta tax cut ultimatum
* Berlusconi seen as big winner in new government
By Gavin Jones and Roberto Landucci
ROME, April 28 (Reuters) - Enrico Letta was sworn in as Italy's new prime minister on Sunday and immediately faced an emergency after an unemployed man shot two police officers outside his office.
The 49 year-old gunman, from the poor southern region of Calabria, told investigators he had planned to attack politicians but had found none within range.
One of the officers was shot in the neck, hitting his spinal cord, and he was in a serious condition, surgeons said. The other was shot in the leg.
In a surreal scene, outgoing Prime Minister Mario Monti received the official trumpet salute in the courtyard of the renaissance Chigi palace before walking across the cordoned-off square, past police crouching over the scene of the shooting, looking for evidence.
There were immediate calls for parties to try to calm a heated public mood that has been exacerbated by deep political divisions as Italy languishes in its longest recession for 20 years and has been without a proper government for months.
"Our politicians have to start providing solutions to the social crisis and to peoples' needs because the crisis transforms victims into killers like the man who shot today," said lower house speaker Laura Boldrini.
"There's a social emergency that needs answers and our politicians have to start giving them."
Letta, 46, who will set out his programme in parliament on Monday, has said his first task will be to tackle the economy which has contracted for six consecutive quarters and pushed youth unemployment close to 40 percent.
Official data this month showed that alongside Italy's 2.7 million officially unemployed in 2012, there were 3 million more who were so demoralised they had given up the search for work, a far higher number than in any other EU country.
The gunman's home town of Rosarno has a jobless rate far above the national average and is renowned for the activities of the local mafia, the 'Ndrangheta, and riots by African immigrants paid a pittance to collect the local fruit harvest.
Having fired several shots at the police on duty outside the prime minister's office, the man, dressed in a suit, shouted "shoot me, shoot me" to other officers nearby, police said.
Letta, on the right of his centre-left Democratic Party (PD), ended two months of stalemate that followed an inconclusive general election by uniting political rivals in a broad coalition government.
The mix of centre-right and centre-left politicians and unaffiliated technocrats has a record number of seven female ministers and is made up by relative youngsters in an atttempt to respond to public disillusion with the political elite.
But the continued risk of political instability was spelled out by an ally of centre-right leader Silvio Berlusconi.
Renato Brunetta, lower house leader of Berlusconi's People of Freedom party (PDL), said the government would fall unless Letta promised in his maiden speech to swiftly abolish an unpopular housing tax and repay the 2012 levy to taxpayers.
"If the prime minister doesn't make this precise commitment we will not give him our support in the vote of confidence," following the speech, Brunetta told daily Il Messaggero.
He said that during negotiations for the formation of the government Letta had "given his word" on the abolition and repayment of the tax, which would gouge an 8-billion-euro hole in public accounts.
New Economy Minister Fabrizio Saccomanni, formerly deputy governor of Italy's central bank, said he wanted to cut public spending and taxes, but made no reference to the housing tax.
In the election, Italians vented their anger at a discredited political class by giving 25 percent of votes to the anti-establishment 5-Star Movement led by former comic Beppe Grillo, which refused to join any coalition.
Divisions have deepened since the vote, with millions of centre-left voters upset, first by a bad split inside the PD and then by the party's decision to govern with Berlusconi after its leadership, including Letta, had ruled out that possibility.
Berlusconi, widely written off after being forced from office in 2011 at the height of a debt crisis, is now a vital part of the ruling majority and has placed several ministers in the cabinet, including the PDL's national secretary Angelino Alfano as deputy prime minister and interior minister.
Recent polls give him a lead of between five and eight percentage points over the centre-left, and many commentators believe he may bring down the government as soon as he is fully confident of winning an election.