Hong Kong and Shanghai were both down in the morning, while Sydney was also lower. Seoul, Singapore, Manila and Wellington edged up while Tokyo and Taipei were flat.
Traders got a positive lead from Wall Street as minutes from the US Federal Reserve's May policy meeting indicated that while officials would likely hike rates by 50 basis points at each of the next 2 gatherings, they were aware of the impact on the economy.
With inflation surging, the central bank - and others around the world - has been forced to tighten policy but that has hammered markets and fuelled fears of a recession.
The minutes also made no mention of a 75-basis-point lift, providing some relief to beleaguered investors.
If inflation gets tame enough over summer, there may not be continued raising of rates
-Carol Pepper of Pepper International on Bloomberg Television
She added that the long-feared era of stagflation - when prices rise but growth remains flat - was unlikely.
"I think we are going to be in a situation where inflation will start tapering down and then we will start going into a more normalised market," she added.