* Ifo business climate index rises in September
* But expectations deteriorate
* Bond yields hold near Monday's week-and-a-half lows
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Recasts after German Ifo survey)
LONDON, Sept 24 (Reuters) - The euro zone's bond yields held near the previous day's week-and-a-half lows on Tuesday after a German sentiment survey failed to ease concern about rising recession risks.
German business sentiment improved in September as companies took a better view of current conditions, but their expectations deteriorated as Europe's largest economy teetered on the brink of recession, the Ifo sentiment survey showed.
The data followed dismal purchasing managers' indexes on Monday. German private-sector activity shrank in September for the first time in more than six years. Growth in services slowed .
A slight improvement in the Ifo business climate index does not suggest a change of trend, the Ifo institute said.
"The outlook index is still pretty dire and while current conditions on the Ifo index showed an improvement, it is still pretty weak," said Chris Scicluna, head of economic research at Daiwa Capital Markets in London.
Most 10-year bond yields in the euro area were higher on the day but within sight of lows hit after Monday's weak PMI data.
Germany's 10-year bond yield was little changed at -0.57% . On Monday, it fell 6 basis points, the biggest one-day decline since June 18, when a dovish speech by ECB President Mario Draghi sent bond yields sharply lower.
"The PMI numbers were devastating, and what concerns us most is that so far we've had a recession of the industrial sector only but now it looks like the services sector is weakening too," said Daniel Lenz, a rates strategist at DZ Bank.
A measure of confidence within French industry showed a dip in September compared with August, France INSEE national statistic office said on Tuesday. It added that other measures of business confidence in France rose, as the euro zone economy battled weak data.
Some caution ahead of a key Supreme Court ruling related to the suspension of Britain's parliament later in the day supported demand for safe-haven assets.
Elsewhere, French central bank chief Francois Villeroy de Galhau said that the European Central Bank's new bond purchase scheme was unnecessary, joining a growing list of public critics since the bank announced it two weeks ago.
(Reporting by Dhara Ranasinghe, editing by Larry King)