* U.S. manufacturing, private payrolls data support sentiment
* European factories also seeing buoyant growth
* World stock prices at record high, Nikkei tops 20,000
* Oil near 3-week low on glut worries
TOKYO, June 2 (Reuters) - Asian stocks edged up on Friday and the dollar bounced from recent lows as upbeat data on U.S. manufacturing and employment and buoyant European factory growth boosted investor optimism.
MSCI's broadest index of Asia-Pacific shares outside Japan ticked up 0.1 percent, while Japan's Nikkei gained 1 percent to top the psychologically important 20,000-point level for the first time since August 2015.
"Market sentiment is very good. The strength in Wall Street shares will be a tailwind for the Nikkei as well," said Masahiro Ichikawa, senior strategist at Sumitomo Mitsui Asset Management.
MSCI ACWI, an index of 46 stock markets in the world, hit a record high, having gained 0.6 percent on Thursday.
The Wall Street's volatility index, which measures implied volatility of stocks and is often seen as investors' fear gauge, fell below 10, near a decade-low touched last month, in another sign of investors' confidence that markets will be stable at least for the time being.
The Institute for Supply Management said its barometer of U.S. factory activity edged up to 54.9 last month from 54.8 in April, while ADP reported private payrolls grew by 253,000 last month, beating analysts' median forecast of a 185,000 increase.
These numbers overwhelmed weakness in auto sales and set markets up for solid numbers in the government's payrolls data due at 1230 GMT.
Following the latest data, the Atlanta Federal Reserve's closely-watched GDP Now forecast model showed on Thursday that the U.S. economy is expected to grow at a 4.0 percent annualized pace in the second quarter.
The spectre of solid U.S. growth led traders to almost fully price in chances that the Federal Reserve will raise interest rates at its June 13-14 policy meeting. They also supported the outlook for possibly another hike by the year-end, likely in September.
That helped the dollar recover in the foreign exchange market.
The dollar firmed to 111.52 yen, from Wednesday's near two-week low of 110.485 yen.
The euro slipped to $1.1218 from Thursday's high of $1.1257, its highest in more than a week.
IHS Markit's Manufacturing Purchasing Managers' Index for the euro zone rose to 57.0 in May, up from April's 56.7 and its highest level since April 2011.
Elsewhere in currency markets, traders are waiting to see if the Chinese yuan extends its recent strong and surprising gains.
The offshore Chinese yuan hit its highest level since October on Thursday, a move traders believe was engineered by Chinese authorities as a show of strength to scare off yuan sellers after Moody's downgraded China last week.
The yuan stepped back to 6.7572 to the dollar from Thursday's high of 6.7245.
Oil prices flirted with their recent lows on concerns that key producers were still adding to the global crude glut.
The Brent futures fell 0.8 percent to $50.24 per barrel, near its three-week low of $49.81 set on Wednesday. (Editing by Kim Coghill)