UPDATE 3-German data, U.S.-China hopes push euro zone bonds to worst session since May

* Ifo survey, positive U.S.-China headlines bolster sentiment

* Poorest session for Italian, German 10-yr bonds since early May

* Italian 10-year yields rise to three-week high

* Euro zone periphery govt bond yields (Recasts, adds details, updates prices)

LONDON, Aug 25 (Reuters) - Safe-haven German government bonds and riskier Italian bonds suffered through their worst session since May on Tuesday as fixed income fell out of favour while German data and optimism on U.S.-China relations boosted risk appetite.

Germany’s Ifo Institute said its business climate index rose to 92.6, its fourth straight monthly increase and stronger than economists had expected, lifting hopes that German companies are recovering from the coronavirus shock.

Analysts said this would be a further sign that Germany’s 130 billion euro ($153 billion) stimulus package is helping power a recovery.

“It does not take a rocket scientist to predict that the (German) economy will have one of its best quarterly performances ever in the third quarter,” said Carsten Brzeski, chief economist for the euro zone at ING.

“All activity indicators point to a continuing increase during the summer months.”

Germany’s revised gross domestic product reading also propped up sentiment. Europe’s largest economy suffered a record 9.7% downturn in the second quarter as private consumption, investments and exports all collapsed in the COVID-19 pandemic, but the reading was better than a 10.1% downturn estimate published last month.

Optimism on U.S.-China trade negotiations, with both sides reaffirming their commitment to the Phase 1 trade deal, boosted risk appetite globally, together with talk of a COVID-19 treatment.

All of that reduced demand for bonds, both higher and lower-rated, and Italian and German 10-year government bond yields saw their biggest daily jumps since early May.

Italian 10-year bond yields were last up 9 basis points after touching a three-week high at 1.11%, while their German peers were up 7 bps to -0.42%.

Earlier they rose to -0.41%, the highest in over a week, nearing the high end of the August trading range of -0.56% to -0.40%.

The closely watched Italy-Germany 10-year yield spread was wider at 151 bps but still below its August high of 158 bps.

Rene Albrecht, a rates strategist at DZ Bank, said Italian bonds were probably taking the biggest hit on Tuesday as a “high-beta” asset, which underperforms the market during a broad sell-off.

In the primary market, Germany sold 4.9 billion euros of two-year bonds in an auction on almost twice as much demand.

Finland said it had appointed banks for a 10-year bond sale via a syndicate of lenders, according to a lead manager note seen by Reuters. The sale will be launched in the near future, subject to market conditions, a phrase usually used a day before a sale.

($1 = 0.8475 euros)

Reporting by Abhinav Ramnarayan and Yoruk Bahceli Editing by Kirsten Donovan and Mark Heinrich