* Macron has pledged to respect 3 pct deficit rule (Adds details)

By Leigh Thomas

PARIS, June 29 France's new government must rein in spending by billions of euros in coming months to live up to its deficit-cutting promises, the public audit office said on Thursday.

Elected last month on pledges to reform the economy, President Emmanuel Macron faces a first major test to find the extra savings deemed necessary by the Cour des Comptes, after the last government overspent the budget in its final months.

Unless cuts are made, the public sector deficit will come to 3.2 percent of economic output this year, exceeding the previous Socialist-led government's 2.8 percent target.

New savings of up to five billion euros ($5.7 billion) would be required if Macron's government is to respect its pledge to post a deficit of 3.0 percent or less this year, honouring an EU-agreed limit for the first time in a decade.

France's fiscal credibility with its European partners and Germany in particular has long suffered from Paris' repeated failure to keep to the EU limit, which it has broken in 12 of the last 15 years.

Last year France posted the biggest deficit in the European Union after Spain, with a budget shortfall of 3.4 percent which the public auditor said was the legacy of years of slower deficit reduction than other states and faster spending growth.

Government ministers had made no secret they expected bad news.

By ordering the audit and preparing public opinion about possible belt-tightening measures, Macron's government is keen not to repeat his predecessor's mistake, who became irredeemably unpopular by raising taxes at the start of his mandate in the face of a gaping deficit.

"Emmanuel Macron has learnt the lessons from Francois Hollande's mistake in mid-2012 who did not communicate enough on the tough situation of public finances," former budget minister Christian Eckert said in a blog post.

The auditor warned that 2018 would be tricky if the government were to trim a further 0.5 percentage points from the deficit as planned, especially as higher spending is expected on security, infrastructure and local authorities.

To keep deficit reduction on track, spending growth would have to be kept to no more than the rate of inflation. It has run 0.9 percent annually on average between 2011 and 2016, the Cour des Comptes audit office said.

Macron's campaign platform included plans for 60 billion euros in budget savings over his five-year term in office, but details are scarce and it also calls for 50 billion euros in investment, as well as tax cuts.

The public auditor said the central state's budget was running 5.9 billion euros over budget. with 2.3 billion of that going to the recapitalisation of nuclear group Areva.

On top of that, the auditor judged that non-tax revenues and receipts from the regularisation of taxpayer assets held abroad had been over-estimated by about two billion euros.

($1 = 0.8776 euros) (Additional reporting by Michel Rose; Editing by Laurence Frost)