* Spreadbetters see softer openings for European markets
* Gauge shows China factory activity skids to 11-month low
* Cautious Fed view on rate hike keeps dollar off recent highs
* Oil slips after rallying overnight on weaker greenback
By Lisa Twaronite
TOKYO, March 24 (Reuters) - Most Asian share markets were set to end a volatile session with modest gains on Tuesday, after a measure of Chinese factory activity dented sentiment by unexpectedly dropping to an 11-month low.
Financial spreadbetters expected softer openings for European bourses, with Britain's FTSE 100 seen opening 15 to 17 points lower, or down 0.2 percent; Germany's DAX expected to open 25 to 26 points lower, or down 0.2 percent; and France's CAC 40 to open 12 to 13 points lower, or down 0.3 percent.
"For today the focus is likely to be on the preliminary flash manufacturing and services PMI data from Germany and France for March, particularly in light of the weak Chinese HSBC manufacturing PMI number," Michael Hewson, chief market analyst at CMC Markets, said in a note.
The China flash HSBC/Markit Purchasing Managers' Index (PMI) dipped to 49.2 in March, below the 50-point level. Economists polled by Reuters had forecast a reading of 50.6, slightly weaker than February's final PMI of 50.7.
MSCI's broadest index of Asia-Pacific shares outside Japan was up about 0.2 percent in choppy trade, pulling higher in the late afternoon after the Chinese figure knocked it off its early highs.
The private survey is likely to add to calls for more policy easing from Beijing, even after two interest rate cuts since November, a reduction in the amount of money banks must keep in reserve and repeated attempts by the central bank to reduce financing costs.
The Shanghai Composite Index ended slightly higher, gaining for a tenth straight day in a rally that has pushed major Chinese indexes to their highest levels in nearly 7 years.
Japan's Nikkei stock average slipped 0.2 percent, pulling away from the previous session's 15-year highs.
"The market is sensitive to good news and is numb to bad news now, but it does seem overbought in a short period of time so profit-taking is natural," said Norihiro Fujito, senior investment strategist at Mitsubishi UFJ Morgan Stanley Securities.
In Japan, a similar manufacturing survey added to concerns that its slowly recovering economy also may be losing momentum, with activity expanding at a much slower clip as domestic orders contracted.
DOLLAR STILL SHY OF RECENT HIGHS
The U.S. dollar edged slightly higher on the day against a basket of currencies, but still remained well off its recent highs as investors bet that the U.S. Federal Reserve will not hike interest rates in the months ahead.
Underscoring that the long-term view remains intact but the near-term is unclear, Fed Vice Chair Stanley Fischer, the Federal Reserve's second-in-command, said on Monday that the Fed is "widely expected" to begin raising interest rates this year though the policy path remains uncertain.
Fischer said the stronger dollar and weaker oil prices figure in U.S. policymaking, but said the central bank is "trying to look through those phenomena."
San Francisco Federal Reserve Bank President John Williams said the high U.S. dollar will be something of a drag on U.S. economic growth this year, but the economy is strong enough to handle it. Williams was addressing an economics conference in Sydney by video link.
The dollar plunged last week after the Fed cut its inflation outlook and its growth forecast. The market consensus is that the Fed will hold off raising rates until at least September, rendering short-term directional bets difficult to make.
The dollar index, which tracks the greenback against six major rivals, edged up about 0.2 percent to 97.179, but remained below its 12-year peak of 100.390 struck on March 13.
The dollar was down about 0.1 percent on the day against its Japanese counterpart at 119.57 yen, well below Friday's session high of 121.20 and levels above 122 yen touched earlier this month.
The euro stood at $1.0918, down about 0.3 percent from the previous session, but still well above a 12-year low of $1.0457 plumbed last week.
The euro got a lift against the dollar on Monday after European Central Bank President Mario Draghi said he expected consumer prices to rise gradually by the end of the year even if they might remain very low or go negative in the months ahead.
The weaker dollar bolstered dollar-denominated commodities, but investors took profits on recent rallies and the China PMI also raised concerns about demand.
U.S. crude futures slumped about 1.4 percent to $46.80 a barrel after soaring 1.9 percent in the previous session. Brent shed about 0.6 percent to $55.59.
Spot gold edged down about 0.1 percent after a four-day rally, to $1,187.80 an ounce.
(Additional reporting by Ayai Tomisawa in Tokyo; Editing by Eric Meijer and Simon Cameron-Moore)