(Updates prices, adds details)

* MSCI World steady after scoring record highs for 7 days

* Wall Street set for flat start, European shares fall

* Japanese stocks powered up by stimulus hopes

* Euro edges up against dollar before Thursday ECB meeting

* Aussie slips even as RBA goes ahead with tapering

MILAN, Sept 7 (Reuters) - World stocks held near record levels on Tuesday supported by bets that the U.S. Federal Reserve will push back tapering its bond purchases and keep its expansive policy for the near-term.

Hopes of extra stimulus in Japan and strong China trade data also provided support, although European stocks retraced ahead of a key ECB policy meeting on Thursday and Wall Street looked set for a soft start after the Labor Day holiday weekend.

By 1100 GMT, the MSCI world equity index was flat after hitting a new record high in Asian hours and following seven consecutive days of gains to record highs.

Europe's STOXX 600 equity benchmark was down 0.4% but just below its lifetime peak hit in August and S&P 500 futures were flat near record highs.

"Now that the tapering announcement from the Fed in September seems unlikely, we should expect 'Goldilocks' markets to continue to at least October or November," said Masahiko Loo, portfolio manager at AllianceBernstein.

The latest rally started after Fed Chair Jerome Powell's dovish speech at the Jackson Hole Symposium in August. It received a further boost from a surprisingly soft U.S. payrolls report on Friday.

The U.S. economy created 235,000 jobs in August, the fewest in seven months as hiring in the leisure and hospitality sectors stalled, reducing expectations that the Fed will opt for an early tapering of its monthly bond purchases.

Speeches by a number of U.S. policymakers later this week will be closely watched for any indication about how the weak jobs report has impacted the Fed's view.

"Given that before Jackson Hole many FOMC members had come out in favour of tapering on a tight timetable, we'll see if they confirm, or align with Powell's more moderate message," said Giuseppe Sersale, fund manager at Anthilia.

Japanese shares rallied further on hopes the ruling Liberal Democratic Party will offer additional economic stimulus and easily win an upcoming general election after Prime Minister Yoshihide Suga said he would quit.

Tokyo's Nikkei crossed the 30,000 mark for the fist time since April, also helped by an announcement on its reshuffle, and the broader Topix index climbed 1.1% to a 31-year high.

Anthilia's Sersale said investors had a defensive positioning on Japanese stocks that led to a short squeeze.

"I was positive on Tokyo (stocks) and remain so, but perhaps at this point it is better to look for a less overbought entry point," he said.

Mainland Chinese shares extended gains, with the Shanghai Composite rising 1.5% to its highest since February, helped by Chinese trade data showing both exports and imports grew much faster than expected in August.

"The mood is improving on hopes the government will take measures to support the economy and that the monetary environment will be kept accommodative," said Wang Shenshen, senior strategist at Mizuho Securities.

A rout in bonds and shares of China Evergrande Group deepened on Tuesday after new credit downgrades on the country's No. 2 developer.

In the currency market, the euro rose 0.06% to $1.1876 , a tad below Friday's one-month peak but still supported ahead of the ECB's policy meeting.

The ECB is seen debating a cut in stimulus, with analysts expecting purchases under its Pandemic Emergency Purchase Programme (PEPP) falling possibly as low as 60 billion euros a month from the current 80 billion euros.

ING strategist Chris Turner said Friday's soft U.S. jobs report and dovish comments last month by Powell have taken "some of the sting out of the dollar’s upside".

"Even the unloved EUR has found a few friends over recent weeks as hawks on the ECB demand a reassessment of pandemic support levels," he noted.

Germany's 10-year yield rose to its highest since mid-July.

The Australian dollar briefly rose after the central bank went ahead with its planned tapering of bond purchases, but quickly gave up those gains after the bank reiterated its need to see sustainably higher inflation to raise interest rates.

The Aussie was last 0.5% lower at $0.7403, off its 1-1/2-month high set on Friday.

Oil prices fell after Saudi Arabia's sharp cuts to crude contract prices for Asia revived concerns over slower demand.

Brent crude futures fell 0.6% to $71.8 per barrel, while U.S. crude futures declined 1.4% to $68.3.

(Reporting by Danilo Masoni in Milan and Hideyuki Sano in Tokyo. Editing by Jane Merriman)