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* Italy's Renzi calls leadership contest
* Italian yields dip after auction, lag peers
* Euro zone periphery yields tmsnrt.rs/2ii2Bqr (Updates prices for close)
By Dhara Ranasinghe
LONDON, Feb 13 (Reuters) - A well-received bond sale helped steady Italian yields after early rises on Monday, but the recovery was limited by uncertainty as former prime minister Matteo Renzi called a leadership contest for his governing Democratic Party.
A rally in equity markets also helped improve sentiment towards the euro zone's lower-rated or riskier bond markets, weakening demand for benchmark German bonds.
Italy sold 8.5 billion euros worth of government bonds, at the top end of the planned issue range.
"The auction was well-received, so that could help reinforce the positive tone towards peripheral markets," said Richard McGuire, head of rates strategy at Rabobank. "But there are still many political risks building up."
Heightened political uncertainty in the euro area has been a major driver of bond yields so far this year, with investors rattled by a strong showing for far-right, eurosceptic candidate Marine Le Pen before the two rounds of France's presidential election in April and May.
Dutch voters go to the polls in March, while Germany holds elections in September.
Italy was in focus on Monday after Renzi said he wanted to hold a leadership contest before any national vote, opening the way for a showdown with his many critics in the group.
Renzi stepped down as prime minister in December after losing a referendum on constitutional reform and wants early elections held this year in an effort to regain power.
However, his drive for a national ballot has been slowed by calls from within the faction-riddled Democratic Party (PD) for him to step aside as party secretary, a post he has held since December 2013.
"The problem in Italy is that there is bit of chaos in that the Democratic Party itself doesn't have a united view on whether it wants snap elections," said DZ Bank strategist Daniel Lenz.
Italy's 10-year bond yield was down 4 basis points at 2.22 percent, having opened the day higher.
The gap to German equivalents remained close to last week's three-year highs.
Yields on other low-rated euro zone bonds in Spain and Portugal fell 4 and 10 basis points to 1.66 percent and 4.04 percent, respectively.
As risk sentiment in global markets in general improved on renewed expectations for U.S. fiscal spending, safe-haven German Bund yields rose 1 bps to 0.34 percent -- edging away from 2 1/2-week lows hit last week.
Greek bond yields also nudged back up as optimism dwindled that the International Monetary Fund and Greece's euro zone lenders had narrowed some of their differences over a bailout package.
Germany on Monday backed Greece to stay in the euro zone and Brussels dispatched a senior official to Athens to persuade reluctant Greeks to take on further reforms to salvage its bailout accord.
In Athens, Yannis Stournaras, Greece's central bank chief, said a swift agreement with international lenders was crucial to keeping the Greek economy on the mend and that down the road "it may be too late".
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets (Editing by Larry King)