By Sam Byford

TOKYO, June 29 (Reuters) - Stocks fell across Asia on Wednesday morning, extending overnight losses on Wall Street amid concerns over recession, inflation and high oil prices, which also boosted the safe-haven dollar.

Japan's Nikkei index fell 1.01% in early trading, while MSCI's broadest index of Asia-Pacific shares outside Japan fell 1.1%, dragged lower by Australian shares , off 1.29%, and Korea's KOSPI, down 1.57%.

Asian shares had ended the previous session on a positive trajectory after China announced an easing of its quarantine requirements for inbound passengers, in what some observes saw as the biggest relaxation so far of its "zero COVID" strategy.

But the impact was petering out on Wednesday.

"Inevitably, markets tend to overreact to these sorts of news," said Carlos Casanova, senior economist at UBP in Hong Kong. "In order for that to be sustainable, we really want to see these measures materialise into actual reopening."

Chinese blue chips which hit a four week high the day before, lost 0.6% while the Hong Kong benchmark fell 1.3%.

The losses in Asia followed a turbulent day on U.S. markets, with the S&P 500 index down more than 2% after data showed U.S. consumer confidence dropped to a 16-month low in June due to fears high inflation could cause the economy to slow significantly in the second half of the year.

Renewed worries over the potential for a global recession sent investors to the safe haven dollar, and the dollar index remained firm at 104.4.

The euro dropped 0.6% on the greenback overnight, and was little changed in early Asia at $1.0529. The Japanese yen stood at 136.03 per dollar, not far last week's 24 year low of 136.7.

The yen has struggled as the Bank of Japan keeps monetary policy loose even as other major banks tighten, a point reiterated by BOJ governor Haruhiko Kuroda on Wednesday.

The yield on 10-year U.S. Treasury notes was flat at 3.1697%.

Oil prices fell back slightly after three sessions of gains, but global supply tightness underpinned the market. An overnight report suggested that Saudi Arabia and the United Arab Emirates are unable to raise output significantly in the near future.

Brent crude futures fell 0.53% on the day to $117.35 a barrel. U.S. crude was down 0.37% to $111.39.

"I think that immediate prices will likely remain elevated," said UBP's Casanova. "But I don't think that we will see a significant spillover onto other Asian asset classes, excluding potentially bonds for some countries that are very sensitive to changes in energy prices."