(Repeats story with Update 1 tag)
* EU's Barroso: healthy public finances needed for growth
* EU Commission asks France to spell out economic plans
* Brussels raises pressure on Rome to act
By Jan Strupczewski
BRUSSELS, June 2 (Reuters) - The European Commission told France and Italy on Monday to stick to their pledges to curb spending while reforming their economies, showing little sign of wavering on EU budget rules.
In its annual policy recommendations to governments around Europe, the Commission sought to strike a fine balance between pushing for budget cuts and stimulating a fragile economy at a time of record unemployment.
The balance is important because the EU has to uphold the credibility of its recently sharpened budget rules and at the same time respond to the rise of extremist parties, which drew new strength in European Parliament elections in May.
"If we keep public finances sustainable, if we keep structural reforms on track, then there is room for more growth and jobs," Commision President Jose Manuel Barroso told journalists.
"The only way to do it is to continue with the necessary fiscal consolidation."
France, whose economy barely grew over the last two years, is an example of the difficulty facing many governments, implementing unpopular structural reforms of pensions or labour laws and keeping a tight rein on public spending.
President Francois Hollande's Socialist Party came third in European elections in May, trailing behind the far-right National Front which took first place and the conservative UMP party as French unemployment hit record highs.
The poor result, which makes it difficult for Hollande to push through any unpopular reforms, also has negative implications for France's credit rating, Moody's agency said.
Hollande is pinning his recovery hopes on plans to phase out 30 billion euros ($40 billion) in payroll taxes on companies in exchange for commitments to hire and invest in France.
Prime Minister Manuel Valls last week promised further tax cuts for low-earning and middle-class households, saying one reason for the rise in support for the National Front was anger at years of tax rises.
But lower taxes mean less revenue at a time when Paris needs to cut its budget deficit to below 3 percent of gross domestic product by the end of 2015 to be in line with EU law. It can hardly expect to get more time because it has already received a two-year extension.
The Commission said that Paris still had time to act to hit the deficit goal, but also asked France to provide more detail on how it aims to bring down the deficit by 2015.
For now, the reduction in the structural deficit - which strips out one-offs, for example - was well below what was needed, it said.
"Moreover, risks to the government's targets are tilted to the downside. In particular, part of the additional measures for 2014 announced in the programme remains to be adopted and the planned amount of savings for 2015 is very ambitious," it said.
"Additional efforts should be spelled out in the forthcoming amending budget law for 2014."
Italy appears to be in a stronger position than France to implement reforms because Prime Minister Matteo Renzi's party won a landslide victory in the European election.
This, coupled with market expectations of policy action by the European Central Bank this week, pushed Italian borrowing costs for five-year bonds to record lows last week.
However, the Commission called on Italy to "reinforce the budgetary measures for 2014 in the light of the emerging gap relative to the Stability and Growth Pact requirement, namely the debt reduction rule."
Renzi has pledged to present a package of measures called "Unblock Italy" by the end of July to try to get the economy moving after a two-year recession.
The legislation would eliminate complicated authorisation procedures for all sorts of economic initiatives and unblock programmes that have been held up for 40 years.
The package adds to an already packed reform agenda for Renzi, who has promised to reform the electoral system, abolish the Senate as an elected chamber and overhaul labour rules, the public administration and the tax system.
So far the most significant measure he has managed to turn into law has been a cut in income tax which will boost pay-packets of low-paid workers by up to 80 euros a month over the second half of this year.
But even though Italy, unlike France, has its budget deficit already safely within EU limits, its debt is the second-biggest in Europe at 135 percent of GDP, which makes it vulnerable to fickle market sentiment.
This leaves the euro zone's third-biggest economy very little room for manoeuvre also in terms of deficit, EU Economic and Monetary Affairs Commissioner Olli Rehn said.
"Italy needs to make an adequate structural effort to tackle its high debt, which is its main vulnerability. It is the structural effort, annually, done by Italy - that's what is important," Rehn said.
Opposition politicians said the EU's call for budget tightening was a slap in the face for Renzi and meant Italy faced further austerity. Economy Minister Pier Carlo Padoan tweeted that the country was on the right path.
"The Commission appreciates Italy's reforms, we knew the debt was high, we will accelerate our reforms and privatisations to reduce it in a sustainable way," he said in the tweet.
The Economy Ministry later issued a statement saying the Commission's assessment did not take into account the government's plans for spending cuts and privatisations which it had not yet fully detailed. (Additional reporting by Robin Emmott and Gavin Jones; Editing by John O'Donnell and Susan Fenton)