Asian share markets were generally in positive territory on Wednesday amid rising COVID-19 cases in mainland China leaving investors unclear over how much the latest breakouts could stall the reopening of the world's second-largest economy.

MSCI's broadest index of Asia-Pacific equities outside Japan was up 0.3% after U.S. markets concluded the previous session with gains. The index is up 12% so far this month.

The majority of the 0.7% increase in Australian equities was attributable to the rise in oil prices, which benefited mining and resources companies. The Tokyo Stock Exchange was closed due to a national holiday.

New Zealand's central bank boosted interest rates by 75 basis points - its greatest-ever move - on Wednesday to a near 14-year high of 4.25% and warned more hikes are on the way as it tries to tame stubbornly high inflation.

Hong Kong's Hang Seng Index was up 0.6% in early trading, while China's CSI300 Index opened relatively flat.

China on Wednesday reported 29,157 new COVID infections for Nov. 22, according to the National Health Commission, compared with 28,127 new cases a day earlier. Case numbers in Beijing and Shanghai are gradually climbing, pushing officials to close several facilities.

"The main story for Asian investors is still China's reopening," said Suresh Tantia, senior investment strategist at Credit Suisse in Singapore.

"We had seen China markets soar up to 20% but those expectations are being dialled back, we think a reopening will be a gradual process and will not be done in a hurry. This indicates that a large number of investors are reducing their exposure to China, lowering their losses or booking whatever profits they may have made on the country."

Meanwhile, the release of U.S. Federal Reserve minutes from its November policy meeting later on Wednesday is being anxiously awaited by investors as they look for insight into how policymakers view economic circumstances.

The Dow Jones Industrial Average increased 1.2% to 34,098.1 on Tuesday, the S&P 500 gained 1.4% to 4,003.58 and the Nasdaq Composite added 1.4% to 11,174.41. Energy equities led the gains, fueled by increased oil prices.

The yield on benchmark 10-year Treasury notes jumped to 3.7578% compared with its U.S. finish of 3.758% on Tuesday.

The two-year yield, which rises with traders' forecasts of increased Fed fund rates, reached 4.5227% compared with a U.S. closing of 4.517%.

The dollar fell against the yen by 0.02% to 141.21.

The euro was trading at $1.0303, up 0.0x?% on the day and up 4.26% over the past month, while the dollar index measures the greenback against a basket of currencies of other key trading partners, was down at 107.14.

"The U.S. dollar lost a little of its recent gains (as) central bankers' consensus over how much more interest rates should climb is fraying," Commonwealth Bank analyst Tobin Gorey wrote on Wednesday.

Smaller or fewer rate hikes may not cause optimism, but they do reduce pessimism.

Oil prices stayed elevated on Wednesday as Saudi Arabia, the world's leading exporter, stated that OPEC+ would sustain output curbs and potentially take more steps to stabilize the market.

In Asian trading, the price of U.S. oil rose 0.3% to $81.15 per barrel. Brent crude increased to $88.35 per barrel.

Gold decreased somewhat. The spot price of gold was $1740.09 per ounce.

While the collapse of the FTX exchange continues to roil cryptocurrency markets, Bitcoin rose 0.33 percent to $16,184 during Asian trading hours.