UPDATE 1-Italian bonds regain their footing, Greece gets debt relief

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr

LONDON, June 22 (Reuters) - Italy's borrowing costs fell on Friday as the government bond market regained its footing after a sharp selloff the previous session, although sentiment remained fragile.

News on Thursday that Italy's new anti-establishment government had appointed two eurosceptics to head key finance committees in parliament revived market concerns about the coalition's commitment to the euro, sending jitters across European markets.

Claudio Borghi, the president of the lower house budget committee, said in a newspaper interview on Friday that Italy's exit from the single currency would solve many of the country's problems, but it is not part of the current government's plans.

While there was a calmer tone to markets, analysts said traders remained sensitive to the headlines coming from Italy - the euro zone's third biggest economy.

Italy's two-year bond yields were down 16 basis at 0.76 percent, while 10-year bond yields fell 8 bps to 2.67 percent -- narrowing the gap over euro zone benchmark issuer Germany.

"Developments in Italy remain major driver for bond markets," said René Albrecht, a rates strategist at DZ Bank. "Sentiment is still fragile and although yesterday's sell off was not as strong as the one in late May, traders are very sensitive to the noise."

Greek bond yields were also lower on Friday after a debt relief announcement.

Euro zone finance ministers on Friday extended maturities and deferred interest of a major part of their loans to Greece along with a big cash injection to ensure Athens can stand on its own feet after it exits its bailout in August.

Greek 10-year bond yields fell 20 bps to 4.11 percent , its lowest level since mid-May, while five-year bond yields fell 25 bps to 3.16 percent.

In broader euro zone bond markets, yields faced some upward pressure from a stronger-than-expected business activity survey from France.

Data compiler IHS Markit said its preliminary composite purchasing managers index, comprising both sectors, rose in June to 55.6 from 54.2 in May.

There was also some focus on an announcement later on Friday regarding early redemptions for the second series of targeted long-term refinancing operations (TLTROs), designed by the European Central Bank to encourage lending to the real economy.

June brings the first early repayment date for almost 400 billion euros of these cheap loans and according to some analysts early repayment could potentially lead to a tightening of monetary conditions in the bloc.

(Reporting by Dhara Ranasinghe; Graphic by Balazs Koranyi; Editing by Toby Chopra)