* China data underpins gains in Asia stocks
* Oil slips on profit-taking, more U.S. budget battles ahead
* Yen recovers from 29-month low versus U.S. dollar
* S.Korea's Kospi underperforms region as automakers slip
* Australia stocks at 19-mth high, Aussie holds gains
By Vikram Subhedar
HONG KONG, Jan 3 (Reuters) - Most Asian stock markets edged higher on Thursday on hopes of a steady economic revival in China, although oil gave back part of the previous session's strong gains as investors took some money off the table and braced for more U.S. budget battles.
The MSCI Asia Pacific ex-Japan index of stocks rose 0.2 percent following Wednesday's 2 percent jump on relief that U.S. politicians had averted the "fiscal cliff".
Data from China showing the services sector expanded in December continued to underpin expectations of an economic recovery that has helped spur a strong rally in Hong Kong-listed Chinese shares over the past month.
The China Enterprises index which rallied more than 4 percent in the previous session eased 0.2 percent. Onshore Chinese markets will resume trading on Friday.
"China looks like it's improving at the margin and the market has momentum that could last for at least a few months," said Christian Keilland, head of trading at BTIG in Hong Kong.
"Investors seem to have accepted that reforms are underway but they're going to happen at a slower pace."
Australian stocks rose 0.7 percent to their highest in more than 19 months, with mining giants Rio Tinto up 2.4 percent and BHP Billiton up 0.8 percent, among the top gainers on the benchmark S&P ASX/200 index.
South Korea's Kospi underperformed the region, falling 0.4 percent as automakers and other exporters slumped on a stronger Korean won, which hit a 16-month high against the dollar overnight.
In other currency markets, the Japanese yen bounced after hitting a 29-month low versus the dollar earlier in the day but analysts warned that any strength is likely to be short-lived.
"Technically dollar/yen looks somewhat overbought here. It's gone a long way in a very short time," said Callum Henderson, global head of FX research for Standard Chartered Bank in Singapore, adding that the dollar could see some consolidation in the near term before heading higher.
The euro which in overnight trading was close to a 8-1/2 month high against the dollar, slipped 0.1 percent.
The U.S. dollar rose 0.2 percent against a basket of major currencies.
President Barack Obama and congressional Republicans face even bigger budget battles in the next two months after a hard-fought deal averted the fiscal cliff of automatic tightening that threatened to push the U.S. into recession.
Strength in the dollar and profit-taking pushed oil prices lower with Brent crude slipping 0.3 percent and U.S crude futures down 19 cents to $92.93.
"After the initial excitement, reality sets in," said Victor Shum, oil consultant at IHS Purvin & Gertz. "There will be other negotiations and the deal is a compromise."