* MSCI AxJ index trades either side of flat

* Dollar strength points to persistent caution

* Asian stock markets: https://tmsnrt.rs/2zpUAr4

SINGAPORE/NEW YORK, Sept 23 (Reuters) - Asia's stock markets struggled to emulate Wall Street's rebound on Wednesday as persistent worries about the global economic recovery kept investors cautious, while ebbing inflation expectations helped the U.S. dollar to a two-month high.

MSCI's broadest index of Asia-Pacific shares outside Japan was steady after two days of declines, but the mood was hardly bullish.

Japan's Nikkei returned from a two-day holiday to drop 0.6%. Markets in Shanghai and Hong Kong opened flat, the ASX 200 <.AXJO rose 1.6% and South Korea's Kospi fell 0.8% on a jump in coronavirus infections.

"I think that reflects a lingering caution. The pandemic is still a concern...non-tech stocks are still weighed down by COVID-19," said Bank of Singapore analyst Moh Siong Sim.

Foreign exchange markets best reflected those worries and a strong dollar kept Asia's currencies on the back foot, extending gains that had begun with hawkish remarks from a senior U.S. Federal Reserve official overnight.

The greenback has busted out of a downtrend that started in March and it rose 0.2% against a basket of currencies to its highest since late July.

It gained by the same margin against the euro and yen and a little further against the Aussie to hit a six-week peak. The kiwi flickered higher after the central bank left rates on hold, as expected, but pressure soon returned.

"There looks to be a squeeze on dollar shorts," said Westpac FX analyst Sean Callow, with jitters in the equity markets, a stalling euro and no new stimulus from the U.S. Federal Reserve to keep it under pressure.

Chicago Fed President Charles Evans, due to become a voter on the Federal Open Market Committee in 2021, said overnight the Fed still needed to discuss its new inflation approach but it "could start raising rates before we start averaging 2%."

That crimped inflation expectations, lifted U.S. real yields and set the dollar rising.

MIXED BAG

The drop and partial recovery of U.S. stocks this week has lacked an immediate trigger though geopolitics, economics and virus news has given investors plenty to worry about.

China-U.S. tensions are simmering, Britain has re-imposed some curbs on restaurants to try and head off a second wave of coronavirus infections and the U.S. election campaign seems to be distracting Congress from passing further aid bills.

Wall Street's Tuesday rebound was led by a 1.7% gain in the Nasdaq as a broker upgrade lifted Amazon.com by nearly 6%. The Dow and S&P 500 made more muted gains of 0.5% and 1% respectively.

Futures trade suggests there is not much conviction behind the bounce, with S&P 500 futures wobbling either side of flat in Asia and Nasdaq 100 futures down 0.5%.

"Care must be taken not to unthinkingly chartacterise this equity bounce back as 'risk on'. It is not," said Vishnu Varathan, head of economics at Mizuho Bank in Singapore.

"At best it is a mixed bag. More likely it was technical buying of dips."

U.S. President Donald Trump told the United Nations General Assembly on Tuesday that China must be held accountable for having "unleashed" COVID-19, prompting Beijing to accuse him of "lies" and abusing the U.N. platform to provoke confrontation.

Another flashpoint, the TikTok deal, is also flaring, with state-backed newspaper China Daily on Wednesday calling the Oracle and Walmart agreement to take stakes in the app "dirty and unfair" and cast doubt on whether it would win Beijing's support.

In commodity markets, oil prices slipped after a surprise rise in U.S. crude inventories. Brent futures were last down 0.9% at $41.34 a barrel and U.S crude futures were down 1% at $39.41 a barrel.

Gold, which has dropped with the rising dollar, was steady at $1,900 an ounce.

(Reporting by Tom Westbrook in Singapore and Suzanne Barlyn in New York; Editing by Sam Holmes and Christian Schmollinger)