MILAN (Reuters) - Italian banking stocks rallied and bonds rose on Tuesday after the country's biggest lender, Intesa Sanpaolo, agreed a bad loan sale at favourable conditions, which investors say could help other lenders achieve better terms and boost lending.

Italian banks still hold some 285 billion euros ($353 billion) in troubled loans four years after a deep recession that had pushed that figure up to 360 billion euros, curbing lending to businesses and raising fears of a big bank failure.

But progress has been made and Intesa's deal demonstrates that appetite for non-performing loans (NPLs) is solid as Italy emerges from years of economic malaise and underperformance versus its European peers.

"We have now finally turned the corner on the aggregate amount of NPL exposure in Italy," said Pierre Bose, head of European strategy at Credit Suisse Wealth Management. Italian stocks graphic: https://reut.rs/2ETyaxO

Sweden's Intrum Justitia will buy Intesa's debt collection unit for 3.6 billion euros in a deal that rids the Italian bank of $13 billion in bad debts, valuing them at 28.7 percent of their nominal value.

Other bad loan sales in Italy have been carried out at 23 percent of nominal value, while another sizeable deal by UniCredit was priced at an estimated 13 percent of nominal value, less than half the value fetched by Intesa.

The deal sent the broader Italian banking index <.FTIT8300> rallying 1.9 percent to a seven-week high and bolstered Italian government debt prices, where the gap on 10-year sovereign borrowing cost over Germany narrowed toward its lowest levels of the year despite a protracted post-election government hiatus.

While Intesa rose 1.5 percent and Intrum gained 8 percent, shares in mid-sized Italian banks Banco BPM, UBI Banca and BPER, which still handle debt recovery in-house, were among the biggest gainers on bets that they could follow in the footsteps of their bigger peer.

"It's very likely that even these banks will decide to put their (debt recovery) business up for sale in order to book capital gains and accelerate derisking," said Giovanni Razzoli, analyst at Italian brokerage Equita SIM.

HELPING REAL ECONOMY

According to his estimates based on terms similar to those agreed by Intesa, a bad loan sale could boost their Core Tier 1 ratio - a key measure of capital adequacy - by between 12 and 27 basis points.

Healthier balance sheets could boost lending and further help the economy, fuelling investor interest for shares in Italian banks, which have undergone a painful restructuring with thousands of job cuts and branch closures over the last years.

"This news is... relevant to the capacity of the banks to provide loans to the real economy, and that feeds through a more bright outlook for the Italian economy," said ING Interest Rate Strategist Martin Van Vliet in Amsterdam.

The restructuring effort and cheap valuations has allowed Italian banks to outperform their peers since early 2017, helping investors to shrug off continued political uncertainty following an inconclusive parliamentary election in March.

Following a stellar 2017, when the Italian economy grew 1.5 percent, nearly twice as much as initial forecasts, the bank-heavy Italian FTSE MIB <.FTMIB> index has risen nearly 8 percent so far this year. That compares with the 2.6 percent drop for the broader European STOXX 600 <.STOXX> stock benchmark.

On Tuesday, the 10-year yield spread over Germany narrowed to two-week lows amid expectations the Intesa deal would bode well for the economy at large as well as potentially reducing somewhat the need for any state backup for the banking system.

S&P Global unexpectedly raised Italy's credit rating late last year in its first such increase for Italy for at least three decades. It cited Italy's strengthening economic outlook, growing investment, a steady uptick in employment and improvements in the debt-laden banking sector for the move.

However, Italy still holds nearly one third of the euro zone's bad loan pile inherited from the financial crisis. A further clean-up could eventually spur consolidation in the country's fragmented banking system.

Elisabeth Rudman, analyst at ratings agency DBRS, said it would be "logical" to expect Italian banks to merge but lenders needed to continue to clean up their balance sheets.

(Removing references to book value and replacing them with nominal value in paragraphs 5 and 6)

($1 = 0.8084 euros)

(Additional reporting by Helen Reid, Fanny Potkin and Dhara Ranasinghe in LONDON and by Claudia Cristoferi and Giulio Piovaccari in MILAN Editing by Gareth Jones)

By Danilo Masoni