June 24 (Reuters) - Euro zone government bond yields were mixed on Monday after the Ifo German business survey showed that business morale unexpectedly fell in June, supporting expectations for interest rate cuts.

The Ifo Institute said its business climate index declined to 88.6 in June from 89.3 in May, compared with analysts' forecast of 89.7 forecast in a Reuters poll.

Germany's 10-year bond yield, the benchmark for the euro area, rose 1.5 basis points (bps) to 2.4126%.

"The Ifo business climate indicator has been overstating the weakness in the economy for some time," said Jack Allen Reynolds, deputy chief euro zone economist at Capital Economics.

"The purchase manager index has been a better guide recently, and while it also declined in June, it still points to a small increase in gross domestic product (GDP) in the second quarter," he added.

Euro zone business growth slowed sharply this month as demand fell for the first time since February, a survey showed on Friday.

On top of that, hopes for monetary easing in Europe strengthened after the Swiss National Bank marginally surprised markets by cutting rates, and the Bank of England delivered a dovish message.

Money markets price in roughly a further 45 bps of European Central Bank rate cuts in 2024, implying another 25 bp cut and an 80% chance of a third cut by year-end. The ECB cut rates for the first time in five years earlier this month.

Italy's 10-year yield fell 1 bp to 3.93%, while the Italian-German yield gap narrowed to 150 bps.

The risk premium over the euro area's most indebted countries tends to decline when hopes for rate cuts strengthen.

The French government bond yield gap versus Germany dipped but remained within striking distance of a seven-year high as investors worry that a far-right election victory could lead the government to increase public spending, fuelling fears of a budgetary crisis at the heart of Europe.

The financial point man for Marine Le Pen's far-right National Rally (RN) told Reuters that an RN-led government would end the decades-long practice of running high budget deficits and stick to the European Union's fiscal rules.

"We believe it's too soon to buy French spreads ahead of the first round of elections, given uncertainty about the shape of a new government and its fiscal policies," said Reinout De Bock, head of European rate strategy at UBS.

"The absorption capacity of French bonds is substantial, but the key question is how a new government will halt the upward trend in debt to GDP," he added.

The gap between French and German 10-year yields - a gauge of risk premium investors demand to hold French government bonds – was at 72 bps. It recently hit around 80 bps, its highest level since February 2017.

The first round of French elections will take place on Sunday.

Market sentiment towards France and the euro area's most indebted countries improved on Thursday as the market got through a French bond auction largely unscathed. (Reporting by Stefano Rebaudo; Additional reporting by Harry Robertson; Editing by Emelia Sithole-Matarise and Mark Potter)