In Japan, the Nikkei 225 tumbled 314.33 points, or 1.3%, to 23,469.39. The Japanese yen traded at 113.24 against the U.S. dollar, strengthening from levels above 114.0 last week.
In Hong Kong, the Hang Seng index dipped 29.66 points, or 0.1%, to 26,172.91
In Australia, major banking names were lower, with Commonwealth Bank shares declining 0.9%. The lender said on Tuesday that it will unwind a controversial system of charging customers commissions on financial product. The changes were sparked by damaging revelations from an inquiry into financial sector misconduct, the news wire reported.
The Australian dollar, meanwhile, traded largely flat at $0.7073 U.S.
CHINA
Chinese markets, however, made a partial recovery after declines in the previous session that followed the country's central bank cutting the reserve requirement for banks over the weekend.
The CSI 300 was down 2.21 points, or 0.1%, to 3,289.69
The People's Bank of China (PBOC) said on Sunday that it was cutting the amount of cash that banks have to hold as reserves by 100 basis points, effective Oct. 15. The reserve requirement ratio (RRR) is currently 15.5% for large commercial banks and 13.5% for smaller lenders.
The move from the PBOC came amid concerns about the economic impact of Beijing's ongoing trade war with Washington.
Officials also said a speech from U.S. Vice President Mike Pence last week was "more hawkish than what people had previously anticipated."
Pence had accused China last week of "malign influence and interference," saying that the country was waging a sophisticated effort to sway the elections against the Republicans in retaliation for U.S. President Donald Trump's trade policies.
China's on-shore yuan was at 6.9203 against the U.S. dollar, near similar levels as the off-shore currency. Before the market opened, the PBOC set the yuan mid-point at 6.9019 against the greenback, which was a bit weaker than a Reuters estimate of 6.8943 per dollar.
In other markets
Korean markets were shuttered for holiday
In Singapore, the Straits Times STI index dumped 14.85 points, or 0.5%, to 3,166.60
In Taiwan, the Taiex index inched up 10.9 points, or 0.1%, to 10,466.83
In New Zealand, the NZX 50 slid 77.12 points, or 0.8%, to 9,069.98
In Australia, the ASX 200 skidded 59.24 points, or 1%, to 6,041.07
