(Adds details on BNL's SIA stake, FSI statement)
MILAN Dec 2 (Reuters) - Italy's two biggest banks, UniCredit and Intesa Sanpaolo, said they would improve their core capital next year by a combined 290 million euros ($395 million) from the agreed sale of their stakes in payment services group SIA.
The deal, which values SIA at 765 million euros, comes as lenders across the euro zone move to sell assets to strengthen their balance sheets ahead of an industry-wide check-up of banks in the euro zone by the European Central Bank.
The two lenders together with Monte dei Paschi di Siena and BNP Paribas's Italian unit BNL have agreed to sell a combined 59.3 percent stake in SIA to Italian state-backed fund FSI, infrastructure fund F2i and asset manager Orizzonte SGR.
Intesa will reap the greater benefit with an expected net capital gain of around 150 million euros that will add 0.06 to 0.09 percentage points to its common equity ratio calculated using so-called Basel III rules, it said in a statement.
UniCredit said separately that a net gain of 140 million euros from selling 20 percent of SIA would have a Basel III common equity impact of around 0.03 percentage points.
Monte Paschi, which is the weakest of Italy's top three banks and is set to launch a rights issue of up to 3 billion euros early next year to repay state loans, said the sale of its 5.8 percent SIA stake would yield a gross 37 million euros.
BNL is selling a 4.5 percent holding.
The deal turns Italy's FSI into SIA's main shareholder with a 42.3 percent stake, for an overall investment of 281 million euros including a 77 million-euro loan.
The fund said in a separate statement it would promote SIA's growth possibly through mergers with domestic or international rivals with an eventual aim of listing it on the stock exchange.
Intesa and UniCredit said they would each retain a 4 percent stake in SIA. ($1=0.7345 euros) (Reporting by Valentina Za; Editing by Greg Mahlich)