NEW YORK/LONDON, Dec 4 (Reuters) - Global shares and the dollar on Thursday were mostly higher as traders await a Fed interest rate cut, although Wall Street stocks were mostly flat after a batch of economic data.

U.S. stocks were lower after two consecutive sessions of gains, with the benchmark S&P 500 falling in choppy trading. Consumer staples, healthcare, and consumer discretionary stocks were suffering the most losses, while industrials, communications services and energy were advancing. 

The Dow Jones Industrial Average fell 0.19%, the S&P 500 dropped 0.10% and the Nasdaq Composite lost 0.03%. 

In Europe, the STOXX 600 was up 0.45% and still headed for a modest weekly gain. London's FTSE 100 index was up 0.19% while Germany's DAX gained 0.32%. MSCI's gauge of stocks across the globe rose 0.23%.

Japanese stocks rallied sharply after an auction of government bonds drew strong demand from investors, which helped set the tone for the broader equity market. The Nikkei rose 2.33%.

"After a 5% pullback in late November, stocks have rebounded and are now trading at the pre-pullback levels and near all-time highs," said Michael Farr, chief executive of investment advisory firm Farr, Miller & Washington in Washington.

Data on Thursday appeared to assuage concerns of a sharp deterioration in U.S. labor market conditions. The number of Americans filing new applications for unemployment benefits fell to a more than three-year low of 191,000 last week.

That came after U.S. private payrolls data posted its biggest drop in more than two-and-a-half years, and following a survey of the services sector that showed activity held steady in November while hiring slowed.

"If they cut rates by a quarter of a point and then take a pause - which every Fed speaker has indicated, markets might be disappointed in the messaging. If they don't cut and say we're going to wait until the next meeting, markets will be disappointed there too," Farr said.

Fed funds futures are pricing a near 90% chance of a quarter-point cut at the end of the Fed's next meeting on December 10, compared with an 83.4% chance a week ago, according to the CME Group's FedWatch tool.      

The dollar index, which tracks the U.S. currency's performance against six others, was up slightly by 0.08% on the day, easing earlier losses and poised to end nine straight sessions of declines.

Oil prices rose, with Brent crude futures adding 0.94% to $63.26 while U.S. crude futures gained, settling up 1.22% at $59.67.

US 10-YEAR TREASURY BOND YIELD UP

The yield on the U.S. 10-year Treasury bond was last up 5.2 basis points at 4.11%. The Financial Times reported on Wednesday that bond investors had expressed concerns to the U.S. Treasury that Kevin Hassett, a candidate to replace Jerome Powell as Fed chair next year, could aggressively cut interest rates to align with President Donald Trump's preferences.

"I think there's purposeful timing by the Trump administration to announce the president's selection of a new Fed chairman that will be seen - correctly or not - as being more dovish around this meeting to appear as an antidote to the messaging," Farr said.

In Japan, the government's debt sale drew the strongest demand in more than six years, which helped soothe investor nerves about the country's long-term finances that have stoked similar worries about other economies.

The dollar was last down 0.16% at 154.97 against the yen, which is heading for its largest weekly gain against the U.S. currency in over two months.

The yen got another boost from a Reuters report that the Bank of Japan is likely to raise interest rates in December with the government expected to tolerate such a decision, citing three government sources familiar with the deliberations.

Meanwhile, the yuan softened a touch, leaving the dollar up 0.17% at 7.069 yuan in offshore trading in Hong Kong. The Chinese currency hit its strongest level against the dollar in more than a year on Wednesday.

Precious metals cooled after a recent hot streak. Gold was flat at $4,207.88 an ounce, while silver fell 2.54% to $56.98 an ounce, after hitting a record high of $58.98 on Tuesday.