* Euro zone bond yields hit six-week highs

* More ECB officials cast doubt on new stimulus package

* Greece, Italy outperform

* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Recasts first sentence with core euro zone bond yields, adds analyst comment, Greek yield, Eurogroup statement)

By Dhara Ranasinghe and Yoruk Bahceli

LONDON, Sept 13 (Reuters) - Core euro zone bond yields rose to six-week highs on Friday as concern crept into the market that the European Central Bank is reaching the limits of what its policy can achieve, a day after the bank pledged indefinite stimulus to boost a weak economy.

Investors had initially cheered the ECB's rate cuts, open-ended asset purchases and steps to protect banks from the negative side-effects of sub-zero interest rates.

But concern then grew over the emphasis at ECB chief Mario Draghi's press conference on the need for fiscal stimulus to take over in boosting economic growth and inflation.

Several ECB officials cast doubt on the effectiveness of and the need for the measures on Friday, including Dutch central bank chief Klaas Knot and Bundesbank President Jens Weidmann .

German, French and Dutch 10- and 30-year bond yields all rose to six-week highs.

Germany's 10-year yield rose 10 bps to -0.45% and was set for its biggest weekly jump since June 2017.

Thirty-year German yields were back in positive territory, trading 11 bps higher on the day at 0.10%.

"The numerous mentions of fiscal policy during the press conference left us with the sense that the monetary policy setters in the euro zone are a little doubtful on their ability to raise inflation without fiscal help," said Peter Chatwell, head of rate strategy at Mizuho.

Euro zone finance ministers are ready to act if the economy takes a turn for the worse, but are not planning any joint fiscal stimulus to complement the European Central Bank's monetary package, their chairman said on Friday.

Analysts said the ECB's plan to resume quantitative easing and offer more generous terms on its cheap multi-year loans to banks was still a good deal for southern European countries.

Italian and Greek bonds outperformed on Friday. Analysts expect spreads between German and southern European debt to keep tightening.

Italy's 10-year bond yield which fell to a record low of 0.758% on Thursday, rose 4 bps to 0.89%. The 50-year yield was up 4 bp to 2.21%.

"The back end of the Italian curve is amazingly stable, which tells you search for yield is on" said Sebastien Galy, senior macro strategist at Nordea Asset Management.

Galy expects Greece to be the primary beneficiary of the ECB's new stimulus package.

Greece's 10-year bond yield fell to a record low on Thursday - at 1.49% - but has bounced back up to 1.58%.

"Because there has been so much destruction [in the Greek economy] there is so much opportunity as things start to turn around, from equities to Greek banks. This creates a very nice development and is far better than would be the case in Italy," Galy said, adding that Italy's current growth potential was discouraging.

Reports that U.S. President Donald Trump does not rule out an interim trade pact with China also brought safe-haven bonds under pressure.

Short-dated bonds were due to close the session flat after coming under pressure earlier on the ECB's tiered interest rates announcement.

The ECB's tiered interest rates, which will exempt banks from paying a penalty charge on idle cash worth six times their mandatory reserves, are expected to reduce demand for short-dated bonds from banks.

(Reporting by Dhara Ranasinghe and Yoruk Bahceli in London Editing by Pravin Char and Matthew Lewis)