* More budget leeway key for Italy's support for Juncker
* EU budget rules already contain needed flexibility
* Germany supports Italy's push for more room for budget manoeuvre
* EU deal with Italy would be blow for Cameron (Recasts with German, Italian comments, background)
By Francesco Guarascio and James Mackenzie
BRUSSELS/ROME June 17 (Reuters) - The European Union, supported by Germany, is working to meet an Italian demand to shift focus from austerity towards growth, in a deal that could help cement Jean-Claude Juncker as the next European Commission president.
Italy's priority is to stimulate weak economic growth, without which it has little chance of reducing its public debt of more than 130 percent of GDP.
Prime Minister Matteo Renzi has made clear he wants to see increased budget flexibility under EU rules. He holds the EU presidency for the second half of 2014.
The European Parliament's Socialists and Democrats group leader Hannes Swoboda indicated on Tuesday that a flexible interpretation of EU budget rules - the Stability and Growth Pact - was a condition for Renzi to back Juncker.
"We are in contact with Renzi. We are trying to formulate a text for how the Stability Pact can be made more flexible without giving up the long term project of reducing debts," Swoboda told a news conference.
"European Council President Herman Van Rompuy is working on a text," Swoboda said. "It's Renzi's condition for any kind of agreement on a candidate."
The deal would be a setback for British Prime Minister David Cameron, who has strongly opposed the candidacy of Juncker, even suggesting that Britain will drift closer to the EU exit if the former Luxembourg leader gets the Commission job.
Renzi's support could have bolstered Cameron's efforts to block Juncker, a federalist, to the EU's most powerful job particularly since the Italian premier's standing has been bolstered by a strong performance in last month's EU Parliament elections.
European Council President Herman Van Rompuy, who chairs EU summits and whose job now is to find out who has the best chance of becoming the next president of the executive European Commission, will see Renzi on Wednesday in Rome.
Germany's Angela Merkel has declared her support for Juncker and Spain's Mariano Rajoy reaffirmed his backing on Monday.
Renzi has said he wants productive investments to be removed from deficit calculations, while Economy Minister Pier Carlo Padoan said this month that reforms being undertaken should be taken into account in the way budget deficits are considered.
Renzi said on Sunday he would support as president of the European Commission someone who "talks about the role of investments, investments in school buildings and broadband".
These are things which he has said he would like to see exempted from deficit calculations.
Renzi appears to have the blessing of Germany, the most ardent defender of EU budget rules.
"I want to make sure that we do everything in our power to make sure that countries that seriously implement reforms should get encouragement and support," German State Secretary for Europe Michael Roth said at an event in the Italian parliament.
He was echoing remarks on Monday from German Economy Minister Sigmar Gabriel, who said he was open to debate on giving EU countries more time and flexibility to meet the bloc's deficit targets as long as they were committed to reforms to boost competitiveness.
EU policymakers say that it is precisely this commitment to reforms that is the most difficult issue.
Last year, France was granted two more years to bring its budget deficit below the EU ceiling, but it did not deliver on its promises of reforms and appears poised to miss the extended deadline.
The chairman of euro zone finance ministers Jeroen Dijsselbloem and EU Economic and Monetary Affairs Commissioner Olli Rehn have been talking about reversing the sequence - first a country undertakes economic reforms by passing laws, and then it gets more time to reduce the deficit.
The Stability and Growth Pact sets a limit on budget gaps at 3 percent of gross domestic product and at 60 percent of GDP for public debt and says every EU country must strive to bring its budget close to balance or into surplus.
Italy's budget deficit has come in bang on the EU's deficit ceiling of 3 percent in the last two years and the EU has ended its disciplinary steps against Rome.
EU budget rules, changed in 2005 under Jean-Claude Juncker's EU presidency, also note that countries trying to reach budget balance, like Italy, should have room for budgetary manoeuvre when it comes to public investment.
The rules also say the EU will take into account implementation of major structural reforms that raise potential growth to help the long-term sustainability of public finances.
Italian government undersecretary for EU Affairs Sandro Gozi noted on Tuesday that sufficient margins for flexibility already existed in the rules even though they had "never been fully exploited due to a restrictive interpretation, partly bureaucratic and partly through mistrust." (Additional reporting by Giselda Vagnoni in Rome, writing by Jan Strupczewski. Editing by Mike Peacock)