(Adds analysis, quotes, stocks on the move)
SYDNEY, Jan 7 (Reuters) - Australian shares rose 0.3 percent on Tuesday, led by bluechip stocks, although sentiment was dampened as Wall Street dipped on a mixed bag of economic data and investors remained cautious about China's growth.
The 'Big Four' banks lifted the market, continuing their stellar run from 2013. Top (Taiwan OTC: 8419.TWO - news) lender the Commonwealth Bank of Australia added 0.3 percent while National Australia Bank rose 0.4 percent.
"Our sense is we see the market back at the 5,700 level by the end of the year," said John Milroy, private client adviser at Macquarie Private Wealth.
"We think there's a real chance of the ASX200 listed companies having a much better revenue outcome than the market expects."
The S&P/ASX (Berlin: AUX.BE - news) 200 index was last at 5,700 in 2008 and is still well below its all-time high of 6851.5, touched in November 2007. The index was trading 14.5 points higher on Tuesday morning (Frankfurt: TDM.F - news) at 5,339.4, after a 0.5 percent fall in the previous session, its biggest one-day drop in three weeks.
The benchmark has recovered from a four-month low of 5,028.2 touched on Dec. 12, and is now hovering some 100 points below a 4-1/2 year high of 5,457.3 hit on Oct. 28.
U.S. stocks slipped on Monday after a mixed batch of economic reports that showed a slowdown in growth in the U.S. services sector and a rebound in new orders for factory goods, dampening local sentiment.
Heavyweight miners dipped after Chinese steel futures fell for a second straight session to hit their lowest in nearly seven months on seasonally tepid demand.
The China HSBC/Markit services sector Purchasing Managers' Index (PMI) dropped to 50.9 in December from 52.5 in November, with business expansion the slowest in six months. China is Australia's top export market.
BHP Billiton Ltd and Rio Tinto Ltd (Xetra: 855018 - news) fell 0.6 percent and 1.6 percent respectively. Iluka Resources Ltd (Other OTC: ILKAF - news) lost 0.7 percent and OZ Minerals Ltd fell 0.8 percent.
Elsewhere, Baraka Energy slumped 40 percent after it disputed the validity of Statoil (Xetra: DNQ.DE - news) 's 2014 work programs on two permits in the Northern Territory, which it said would need to be resolved by arbitration.
Dairy group Murray Goulburn said it expects a regulatory decision on its offer for Australia's Warrnambool Cheese and Butter Factory Holdings Co by the end of February, a shorter time-frame than initially expected. Warrnambool was down 0.1 percent.
New Zealand's benchmark NZX 50 index rose 0.3 percent or 14.8 points to 4,780.1.
(Reporting by Thuy Ong; Editing by Richard Pullin)