* Portugal's BES says not at risk of running short of capital
* Greek, other peripheral euro zone bond yields also fall
* Italy sells 7.5 billion euros of bonds to strong demand (Updates with Italian auction result, adds fresh comments)
By Emelia Sithole-Matarise
LONDON, July 11 (Reuters) - Portuguese bond yields fell on Friday as the country's biggest bank sought to reassure investors about its financial stability after concerns over the health of its parent company rattled financial markets this week.
Investor worries about losses on loans to the parent company of Banco Espirito Santo accelerated a sell-off in Portuguese assets this week that triggered the first significant episode of contagion this year in peripheral euro zone bonds.
The bonds recovered some poise after Banco Espirito Santo said on Thursday night that losses on loans to the troubled business empire of its founding family would not put BES at risk of running short of capital.
The calmer market backdrop enabled Italy to sell 7.5 billion euros of bonds, the top of its targeted range, at a solid auction, which sharply contrasted with Greece's three-year bond sale on Thursday where demand was hurt by fallout from Portugal.
The Italian sale demonstrated the enduring investor search for relatively higher returns still offered by the larger, liquid debt markets of Italy and Spain, despite a two-year rally that has driven borrowing costs to record lows.
Yields on Portuguese 10-year bonds were down 10 basis points at 3.92 percent. They had risen about 40 bps this week, their biggest weekly increase this year.
"It (the sell-off) was a bit overblown. After the huge rally behind us in non-core bonds as well as equities, we've had a multitude of bad news ... and so the market clearly needed a trigger for profit-taking and that's what happened," said Jan von Gerich, chief fixed income analyst at Nordea.
"For now at least, sentiment will remain nervous but I don't think it's something that will reverse the general downward trend in peripheral bond yields."
Yields on bonds issued by bailed-out Greece, whose three-year debt sale on Thursday saw poor demand amid the market rout, were 4 bps lower at 6.28 percent.
Italy sold three- and 15-year bonds at record low yields as persistently abundant liquidity appeared to overshadow the bank problems in Portugal.
European Central Bank interest rate cuts last month and its upcoming largesse to banks via cheap four-year loans to banks later this year is fostering demand for debt from the euro zone periphery as yields on top-rated bonds dwindle. Latest data also showed the recovery in countries like Spain remaining on track as growth stutters in Germany and France.
"We think those common factors will outweigh local factors, including the renewed concerns about the Portuguese banking sector, and we remain overweight in peripheral bonds, focusing on shorter maturities," said Seamus Mac Gorain, a portfolio manager at JPMorgan Asset Management.
Italian 10-year yields were 4 bps down at 2.90 percent. Spanish equivalents were 2 bps lower at 2.80 percent. (Editing by Larry King and John Stonestreet)