By Selena Li

HONG KONG, June 21 (Reuters) - Asian stocks and U.S. share futures turned higher on Tuesday as the market took stock after a recent steep selloff, but concerns remain that aggressive central bank rate hikes to curtail inflation could spark a global recession.

MSCI's broadest index of Asia-Pacific shares outside Japan rose 0.85% in early trading, edging up from a more than five-week low hit the previous day.

Japan's benchmark Nikkei average opened up 1.16%, and Nasdaq and S&P500 e-mini share futures each rose nearly 1.5%.

"I think the green that we're seeing this morning is not necessarily a function that people are moving back in towards risk assets," said Kerry Craig, global market strategist at JPMorgan Asset Management.

"It's just the normal behavior on the very large selloff to get some reprieve and breathing space come through because fundamentally, nothing has changed on the macro front last week."

Chinese blue chips rose 0.5%.

Central banks around the world are looking to raise interest rates aggressively to curb rising inflation, a sentiment underscored on Tuesday by Reserve Bank of Australia (RBA) Governor Philip Lowe, who pointed in a speech to further rate hikes.

"As we chart our way back to 2 to 3% inflation, Australians should be prepared for more interest rate increases," Lowe warned. "The level of interest rates is still very low for an economy with low unemployment and that is experiencing high inflation."

Still, Australia's S&P/ASX 200 index climbed 1.12% in early trading. The Australian dollar rose 0.3% on the news before paring gains.

The euro also gained 0.25% on the improved risk sentiment, after European stock markets chalked up modest gains on Monday to recover a little from last week's hefty losses. U.S. markets were closed for a holiday.

The dollar index, which tracks the greenback against six major peers, eased slightly to 104.29. The Japanese yen remained under pressure at 135.07 yen per dollar, not far off a 24-year low of 135.58 yen hit early last week.

In bond markets the yield on U.S. benchmark 10-year treasury notes was 3.2976%, up a little from last Friday's close.

Last week's peak of 3.495% was the 10-year yield's highest since 2011, and came the same day the Fed raised interest rates by a massive 75 basis points.

Oil prices swung higher with traders focusing on tight supplies over slowing global economic growth. U.S. crude rose 2.12% to $111.88 per barrel and Brent was at $115.56, up 1.25% on the day.