By Valentina Za

MILAN (Reuters) -The Italian arm of France's Credit Agricole has started offering fixed-term savings accounts to win new customers in its biggest foreign market, at a time when competition for cash among the country's lenders grows.

With deposit rates lagging soaring lending costs, banks have posted record earnings in recent quarters, prompting Rome's conservative government to threaten the industry with a tax on windfall profits if they fail to improve savers' returns.

Credit Agricole Italia is currently advertising an account paying 3.5% over 12 months, a rarity among high street banks in Italy where only digital lenders have been offering these type of time deposits to retain savers.

Such accounts are common in France, where lenders are subject to government-imposed increases to the rates paid on the most popular type of savings.

"French banks are used to time deposits as a funding tool, so it makes sense for them to use the same tool on a different market," said Milan's Cattolica University Professor Rony Hamaui, noting that current accounts make up only 35% of total deposits in France compared with 72% in Italy.

France has Europe's highest proportion of savings accounts with a fixed term or requiring notice to withdraw, Italian banking association ABI told Reuters based on central bank data. That share is 15.4% of total assets in France, against Italy's 13.8% and a euro zone average of 14.7%.

Executives at two Italian banks said Credit Agricole Italia's move was aimed at wooing new customers but added their own lenders' liquidity and market share was such that they would not follow for now.

Credit Agricole Italia declined to comment. The French bank is also the main investor in Italy's Banco BPM.

Challenger banks, which don't have branches and are more exposed to competition, still provide the best deals on bank account comparison website ConfrontaConti.it.

However, "we've noticed that some 'traditional' banks have started offering time deposits with rates...that are not particularly aggressive," ConfrontaConti.it said in reply to a Reuters query.

Italy's BPER recently started offering a gross yearly rate of 4.25% to those depositing 30,000 euros and investing 15,000 euros in asset management products, still far below Italy's annual inflation rate, which stood at 7.6% in May.

While some Italian banks have moved to scrap current account costs, they have stopped short of paying interest on cash they say people keep there for day-to-day transactions, instead offering investment products such as money market funds.

Some have also offered time deposits to wealthy clients using private banking services or to corporate clients.

Deposits returned an average 0.68% in May, with 0.32% on current accounts and 3.21% on time deposits, up from 2.93% the previous month, ABI data showed.

Rising competition from government bonds, which the government is targeting specifically at retail investors, is piling pressure on Italian lenders, which have just repaid some 140 billion euros of long term European Central Bank loans.

"Traditional banks still have an advantage over digital-only lenders but in the coming six to 12 months this will change as the ECB mops up liquidity. The value of deposits will increase, which is a good thing for depositors," Hamaui said.

(Reporting by Valentina Za; editing by Kirsten Donovan)