"This means upside risk to tomorrow's payroll report but please remember how the ADP is known for throwing the market off ahead of the official jobs report," said Jennifer Lee, senior economist at BMO Capital Markets.
In Europe, the FTSE 100 index of leading British shares rose 0.2 percent to close at 6,816.37 while the CAC-40 in France fell 0.4 percent to 4,444.72. Germany's DAX rose 0.1 percent to 9,911.27.
In the U.S., the Dow Jones industrial average was up 0.1 percent at 16,967.53 while the broader S&P 500 index rose the same rate to 1,974.68.
Earlier, in Asia, investors were encouraged by surveys showing China's manufacturing activity improved in June for the first time in six months. That came on top of the government's decision to expand credit by allowing banks to lend more relative to the size of their deposits.
Asia's heavyweight, the Nikkei 225 in Tokyo, gained 0.3 percent to 15,369.97 while China's benchmark Shanghai Composite Index added 0.4 percent to 2,059.42.
Hong Kong's Hang Seng jumped 1.5 percent at 23,549.62 while Seoul's Kospi added 0.8 percent to 2,015.28 and Sydney's S&P/ASX 200 rose 1.5 percent to 5,455.40.
Elsewhere, the euro was down 0.2 percent at $1.3655 a day ahead of the monthly policy meeting of the European Central Bank. Though no change in policy is expected, traders, particularly in the currency markets will be interested to hear what ECB President Mario Draghi says in his ensuing press conference about the state of the 18-country eurozone economy.