SYDNEY, Dec 1 (Reuters) - Asian shares edged lower, starting the last month of the year on a weak note after recent rally, although anticipated interest rate cuts in Europe and the United States should help ease pressure on local currencies and central banks.

MSCI's broadest index of Asia-Pacific shares outside Japan fell 0.4% after a surge of 7.3% last month, the most since January. Japan's Nikkei was flat, having also jumped 8.5% in November in the best month in three years.

Europe, however, set to open higher, helped by wagers of early and aggressive rate cuts by the European Central Bank after surprisingly soft inflation numbers. EUROSTOXX 50 futures rose 0.4% and FTSE futures gained 0.6%.

"Our sense is that quite a lot of the good news is already in the price. A little bit of profit-taking and rebalancing have probably played in the month-end, obscuring the messaging we typically get from the price action," said Rodrigo Catril, a senior FX strategist at the National Australia Bank.

Oil prices, which slid more than 2% overnight as output cuts by OPEC+ producers underwhelmed, remained subdued even as Israel's military said it has resumed combat against Hamas in the Gaza Strip, after a seven-day truce, raising the prospect of renewed violence in the Middle East.

Brent crude futures slipped 0.2% at $80.67 a barrel while U.S. West Texas Intermediate futures was little changed at $75.94 a barrel.

Regional surveys of purchasing managers showed factory activity in Asia remained weak. Japan's factory activity shrank at the fastest pace in nine months while South Korea's factory activity were unchanged after 16 months of contraction.

Mixed factory activity data for China pointed to still feeble economic recovery in November. Chinese bluechips fell 0.2% and Hong Kong's Hang Seng index dropped 0.1%.

S&P 500 futures eased 0.1% and Nasdaq futures fell 0.2%.

Overnight, data showed that both U.S. and European inflation are cooling as desired. Benign data on U.S. inflation reinforced market expectations for about 115 basis points in rate cuts from the Federal Reserve next year, with a first move fully priced in for May.

The major surprise was with euro zone inflation, which missed forecasts by a large margin, triggering a slide in the euro and prompting markets to price in rate cuts of about 110 basis points next year, commencing as early as April.

Goldman Sachs now expects the ECB to deliver its first interest rate cut in the second quarter of 2024, compared to an earlier forecast of a cut in the third quarter.

Traders are now waiting for Fed Chair Jerome Powell's Q&A appearance on Friday, with bulls betting the central bank chief will accommodate market wishes.

"We suspect this will be a very tightly choreographed session and will stick to the pre-Waller script of caution when it comes to further hikes but with no hint of easing," said Robert Carnell, regional head of research, Asia-Pacific, at ING.

Fed Governor Christopher Waller, deemed a hawk, this week hinted at lower interest rates in the months ahead if inflation continued to ease.

Declining interest rates in Europe and the U.S. would be good news for Asia, greatly easing the pressure on emerging market currencies. Investors are turning more bullish on Asian currencies, a Reuters poll found.

The dollar index was on the back foot at 103.32 on Friday after jumping 0.6% overnight, supported by a sliding euro on ECB's rate cut expectations. It fell 3% for November, the worst in a year.

The euro recovered some lost ground in Asia and was last up 0.2% to $1.0903, after tumbling 0.7% overnight.

U.S. Treasuries also eased a little after the best month since 2011. The yield on 10-year Treasury notes slipped 2 basis points in Asia to 4.3320%, on top of a plunge of 52.2 basis points for the month.

Two-year Treasury yields fell 4 basis points to 4.6771%.

Gold prices was 0.26% higher at $2,041.29 per ounce.

(Reporting by Stella Qiu; Editing by Jamie Freed and Miral Fahmy)