* Investors relieved Renzi's party leads in EU vote
* Italy yields set for biggest one-day fall in 7 months
* French yields steady, market shrugs off National Front win
* Focus on fact pro-EU parties dominant in parliament (Updates prices, adds fresh comments)
By Emelia Sithole-Matarise
LONDON, May 26 (Reuters) - Italian bond yields slid on Monday after Prime Minister Matteo Renzi's centre-left Democratic Party triumphed in European parliamentary elections, strengthening his mandate to push for economic reforms.
The yields were set for their biggest one-day fall since October 2013, with Renzi one of the few leaders across Europe to have scored a victory against Eurosceptic nationalists who stunned mainstream parties in France and Britain on Sunday.
Critics of the European Union more than doubled their seats in a continent-wide protest vote against austerity and unemployment but bond investors focused instead on the fact that the majority of seats would be held by parties supporting the European Union.
Renzi's party handily beat the anti-establishment 5-Star Movement, a relief for investors concerned that a closer result would weaken Renzi's drive through of the swift reforms he promised when he took power.
Italian bonds outperformed most of the market, with 10-year yields dropping 14 basis points (bps) to 3.02 percent, while their Spanish equivalents were 8 bps lower at 2.91 percent. Traders said intra-day moves could be exaggerated by thin volumes, with UK and U.S. markets closed for holidays.
"In Italy the biggest party in the government has gained ... The current prime minister will come out strengthened so they can continue to deliver reforms that are needed by the country," said ING strategist Alessandro Giansanti. "That's why you see a sharp tightening of spreads."
Greek 10-year yields were also set for their biggest one-day drop since January, after the anti-austerity Syriza movement won the vote but failed to deliver a knockout blow against Prime Minister Antonis Samaras's government that some had feared.
The yields were last 30 bps down at 6.23 percent , reversing some of last week's rise. Investors had been concerned that strong gains by Syriza could force Samaras, whose ruling coalition has a slim two-seat majority in the national parliament, to hold fresh elections.
A credit rating upgrade on Friday by Fitch to B from B- with a stable outlook also bolstered sentiment in Greek bonds.
Yields on Irish and Portuguese bonds, which were at the centre of the euro zone sovereign debt crisis two years ago, were 7 bps lower at 2.71 and 3.72 percent respectively, as their ruling parties held ground in the weekend polls.
"We have not seen spectacular outcomes in terms of Eurosceptic parties in the weaker countries except for Greece ... and that seems enough to draw investors back," said Christian Lenk, a fixed income strategist at DZ Bank.
French yields held steady at 1.83 percent, with some in the market saying investor relief that Moody's had refrained from updating on the country's creditworthiness at a scheduled review on Friday overshadowed unease at the National Front's poll triumph. Moody's rates France Aa1 with a negative outlook and there had been market speculation of a downgrade.
Other analysts said the National Front's strong showing in the EU elections was largely expected as the Socialist Party has gradually lost ground over the past year. The market was also supported by expectations of fresh monetary stimulus when the European Central Bank meets next week.
"We doubt that the outcome will result in a marked spread widening, but the performance of French government bonds will be watched closely today with risk of underperformance," Commerzbank strategists said in a note. (Editing by Greg Mahlich)