Japan's broad Topix index of shares climbed for a second straight day on Thursday as higher energy prices boosted commodities producers, while chip-related stocks weighed on the benchmark Nikkei gauge.
Australian shares edged higher on Wednesday after a sharp drop in the previous session, as traders awaited quarterly economic growth data due later in the day for further direction.
Japan's Topix index reached a 33-year high on Tuesday as chip-related stocks tracked overnight gains on the Nasdaq, with sentiment further boosted by optimism that Washington could reach a debt ceiling deal.
China stocks rose on Tuesday after the central bank cut the amount of cash banks must hold in reserve, while investors cautiously watched if Evergrande would default as the world's most indebted developer inches closer to a debt restructuring.
Japanese stocks fell on Monday, tracking the Dow's losses at the end of last week amid renewed coronavirus concerns, while chip-related shares followed their U.S. peers higher.