* Italian yields at 3-month low, slide for 2nd straight day
* Expectations of snap Italian vote ease, lift sentiment
* Euro zone markets little changed after UK election shock
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates price move, adds comment)
LONDON, June 9 (Reuters) - Italian government bond yields tumbled to three-month lows and were on track to end Friday with their biggest weekly fall this year as a failure to reach an agreement on a new electoral law was seen reducing the chances of early parliamentary elections.
Across the euro zone, safe-haven bond yields were pinned near multi-month lows after Thursday's snap election in Britain left the ruling Conservative party without a majority in parliament just as talks to exit the European Union loom.
In contrast, the prospect of early elections and political uncertainty in Italy - the euro zone's third biggest economy - appear to have ebbed this week, boosting sentiment towards Italian assets.
The head of the country's ruling Democratic Party, Matteo Renzi, said he was pessimistic over the chances of reaching a new cross-party pact on a reform of the electoral law. That came a day after a deal between Italy's top four parties unraveled in parliament.
President Sergio Mattarella, the only figure with the power to dissolve parliament, has demanded new voting rules be drawn up because at present there is too much divergence between the systems for electing members in the upper and lower chambers.
"There has been a lot of pressure on Italian bonds over the last few weeks because the idea of going to elections this year was not welcome for investors," said UniCredit strategist Luca Cazzulani in Milan. "Because this is now being put under question, the move is retracing."
Italy's 10-year government bond yield tumbled 8 basis points (bps) to a three-month low of 2.09 percent, adding to a 12 bps fall on Thursday.
That left yields on track for their biggest one-week fall since mid-December and their biggest two-day slide since October 2015.
The gap between Italian and German bonds yields, a gauge of how investors view relative risks, narrowed to around 183 bps. That's down from more than 200 bps earlier this week.
Signs this week of progress in addressing weakness in Italian banks and comfort that the European Central Bank shunned talk of unwinding its stimulus scheme at a policy meeting on Thursday also lifted sentiment towards Italian assets.
"We've had some good news on the banking sector this week, a shrinking likelihood of snap elections and a positive ECB meeting, so all of this is helping BTPs," said DZ Bank strategist Christian Lenk.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.bi z / c m s / ? p a g e I d = l i v e m a r k e t s
(Reporting by Dhara Ranasinghe; Editing by Mark Potter and Toby Davis)