* World stocks at 2-month highs but European shares dip
* U.S. stock futures flat to slightly positive
* Oil prices off day's lows
* Focus turning to U.S. ISM non-manufacturing data
* U.S. dollar, Aussie dollar gain (Writes through)
By Dhara Ranasinghe
LONDON, March 3 (Reuters) - World stock markets touched two-month highs on Thursday as easing concern about the global growth outlook and a recovery in commodities lifted risk appetite globally.
Upbeat data from major economies this week and signs of a rebound in a range of commodities have helped restore some calm to global markets after a turbulent start to the year.
Growth in Germany's private sector slid to a five-month low in February but remained solid, underpinned by growing services, a survey showed on Thursday.
MSCI's world equity index rose to its highest level in two months, the pan-European FTSEurofirst 300 stock index dipped 0.3 percent but held within sight of Wednesday's one-month peak.
U.S. stock futures meanwhile pointed to a largely unchanged start for Wall Street shares .
That followed a strong session in Asia, where MSCI's broadest index of Asia-Pacific shares outside Japan added another 1.1 percent to reach a two-month peak.
"For markets to continue to move higher, more good data - especially out of the U.S. - will be needed," said Markus Huber, a trader at City of London Markets.
Focus turned to the U.S. non-manufacturing ISM report due at 1500 GMT, with investors eyeing the employment component for clues about Friday's non-farm payrolls report.
A solid jobs report could bolster expectations that the Federal Reserve remains on track to raise interest rates this year.
Data on Wednesday showed U.S. private-sector jobs rising a surprisingly strong 214,000 in February, adding to speculation that the payrolls report would also be upbeat.
OIL DIPS, COPPER FIRM
Oil prices eased after ballooning U.S. crude inventories and a lack of any fresh action from the world's largest producer to temper supply snuffed out some of the bullish sentiment that has built this week.
Brent crude prices slipped 0.2 percent to $36.86 but are still some 35 percent above last month's lows. U.S. crude futures were marginally higher at $34.68. They have risen more than a third since Feb. 11, when prices dropped to levels not seen since 2003 at just over $26 a barrel.
Copper prices hit their highest in more than three months, boosted by higher equities and some confidence in global growth prospects.
Risk appetite also remained strong in currency markets, with the Australian dollar hitting a two-month high and the safe-haven yen ceding ground to the U.S. dollar and the euro.