Japan's benchmark index hit a new 26-low on Tuesday, following after another selloff on Wall Street.
The Nikkei-225 index slipped 31.05 points, or 0.44%, to 7,054.98, ending at the lowest level since October 1982 for a second straight day.
The broader Topix index of all first-section shares fell 7.03 points, or 0.99%, to 703.50.
In New Zealand, the NZX 50 was down 6 points, or 0.26%, to 2462 on turnover of $73 million.
Top stocks were mixed. Telecom lost 2 cents to close at $2.35, Contact Energy fell 5c to $5.60, while Fletcher Building was up 2c to $5.15.
In Australia, the market overcame a negative start to close higher, boosted by stronger energy and financial sectors, but the volume of trading was low.
The benchmark S&P/ASX200 index was up 30 points, or 0.95%, at 3,184.5, while the broader All Ordinaries gained 21.5 points, or 0.69%, to 3,143.2.
US markets down
In the United States on Monday, the Dow Jones industrial average fell 79.89 points, or 1.21%, to 6,547.05.
The S&P 500 index lost 6.85 to 676.53, while the Nasdaq composite index fell 25.21, or 1.95%, to 1,268.64.