* Investors cheer ECB hints at bond purchase adjustments
* Leadership contest seen delaying explosive Italy election
* French yields up on prospect of socialist election tie-up
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates prices)
By John Geddie
LONDON, Feb 17 (Reuters) - Italy's benchmark government bond yield was set for its first weekly fall for over a month on Friday as investors pushed back their expectations for elections and tipped the country to benefit more from central bank debt purchases.
While the country's benchmark 10-year yield edged up on the day, it remained near a three-week low struck Thursday after the European Central Bank kept the door open to changing the proportion of bonds it buys from each country.
The ECB currently weights its purchases based on the size of a country's economy, meaning the lion's share of buying is in Germany, but investors expect any deviation from that could benefit countries with the biggest debt pools such as Italy.
Investors in Italy have been beset by political worries since the resignation of Prime Minister Matteo Renzi last December as it potentially paves the way for new elections in which the eurosceptic 5-star Movement could be contenders.
Renzi's call this week for a leadership contest in his ruling party appears to have brought some respite as it is seen as potentially delaying those elections.
A prominent Italian minister said on Friday it would be impossible to hold a national election in June unless Renzi backed down.
"The mood was improving in the first half of the week for Italian bonds and Renzi was a factor in that but the largest part of the movement came after the ECB minutes," said Luca Cazzulani, a rates strategist at UniCredit (EUREX: DE000A163206.EX - news) in Milan.
Italian 10-year bond yields edged up 3 basis points (bps) to 2.18 percent, only giving up some of the 16 bps fall seen on Thursday that pushed yields to a near three-week low of 2.13 percent.
Yields were set for around a 9 bps drop on the week, their first weekly fall in five.
The gap (Frankfurt: 863533 - news) between Italian and German bond yields - which moved lower on the day to 0.31 percent - sat at around 187 bps, well off a three-year high of over 200 bps hit 10 days ago.
Friday's rise in Italian yields came during a corresponding rise in French yields as a new twist in the race for the France's presidency rattled investors.
The two main left-leaning candidates in the election are holding talks on possible cooperation, a move that could potentially put one of them in contention to reach the crucial election run-off.
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 Keith Weir and Mark Potter)