* Oil up on Iran unrest, strong global economy
* U.S. service sector survey, German jobless rate upbeat
* Fed minutes show policymakers unsure of tax cut impact
TOKYO, Jan 4 (Reuters) - Asian shares scaled a 10-year high on Thursday as solid economic data from the United States and Germany reinforced investors' optimism while oil prices hovered at 2-1/2-year high with unrest in Iran stoking supply disruption concerns.
MSCI's broadest index of Asia-Pacific shares outside Japan ticked up 0.1 percent, coming near its 2007 peak, with Australian shares hitting a decade high.
Japan's Nikkei jumped 2.0 percent on its first trading day of the year while the broader Topix hit its highest level since 1991.
"The economic data published over the holiday period has been pretty good. So for those who were worried about new year profit-taking, the market would look pretty strong," said Hirokazu Kabeya, chief global strategist at Daiwa Securities.
The economic data published on Wednesday on both sides of the Atlantic reinforced investors' expectations that solid global growth will boost demand of goods including oil and lift corporate earnings.
U.S. factory activity increased more than expected in December, boosted by a surge in new orders growth, in a further sign of strong economic momentum at the end of 2017.
In Germany, Europe's economic power house, the unemployment rate hit a record low of 5.5 percent in December, underpinning a broad-based economic upswing.
The world's stock markets hit a record high on Wednesday.
On Wall Street, the three main stock indexes hit record closes, helped by a 1.5 percent rise in energy stocks.
Oil prices hovered at 2 1/2-year highs as the anti-government protests in Iran that began last week rattled Tehran's clerical leadership and left 21 people dead so far, raising concerns about supply.
U.S. West Texas Intermediate (WTI) crude futures traded at $61.84 per barrel, having risen to as high as $61.97 a barrel, their highest level since June 2015.
Still, investors are expecting markets to be stable, with Cboe Volatility index, which measures implied price volatility of U.S. stocks in the next one month, closing at 9.15, just above record closing of 9.14 touched on Nov 3.
In the past few months, the volatility index has been kept at one of the lowest levels since the global financial crisis in 2008.
That is primarily because investors bet the U.S. Federal Reserve and the world's other major central banks will tighten monetary policy only gradually with few signs of inflation pressures building.
The minutes of the Fed's last policy meeting on Dec. 12-13 released on Wednesday did little to change that perception.
They showed policymakers saw President Donald Trump's tax cut plans as providing a boost to consumer spending but also uncertainty over the impact of fiscal stimulus on raising price pressures.
The price of Fed funds rate futures fell a tad, with April contract pricing in about 75 percent chance of a rate hike by March, compared to around 60 percent at the end of last year.
In the currency market the dollar ticked up 0.2 percent against the yen to 112.69 yen following the upbeat U.S. data while the euro was little changed at $1.2002.
(Editing by Sam Holmes)