Greek Prime Minister Antonis Samaras failed to get enough support for his presidential nominee on Monday and will call an election for 25 January.
The price of copper also fell to its lowest in four-and-a-half years on a strong dollar and a slowdown in China.
Japan's Nikkei fell 1.6% to 17,450.77 on its last trading day this year.
But the index ends the year up 7.1%, driven by aggressive asset purchases by the Bank of Japan and a weaker yen that boosted company profits.
The dollar was at 120.41 yen from 120.66 yen in morning trade.
Japanese markets will be shut for the reminder of this week and will reopen next Monday.
China shares traded in opposite directions with Hong Kong's Hang Seng index down 0.9% at 23,550.44.
On the mainland, the Shanghai Composite bucked the trend and was up 0.7% to 3,189.64.
In Australia, the benchmark S&P/ASX 200 closed down 1% to 5,416.6 after gaining 1.5% on Monday.
Shares of heavyweight miners BHP Billiton and Rio Tinto were both down more than 0.7% on falling commodity prices.
South Korean shares were lower despite economic data showing signs of the economy picking up.
The country's industrial output rose by a seasonally adjusted 1.3% in November from October, just beating expectations and marking its fastest rise in four months.
Meanwhile, its current account surplus was also up to a seasonally adjusted $9.73bn (Â£6.2bn) in November - its highest in seven months.
But the benchmark Kospi closed down 0.6% to 1,915.59, down 4.8% for the year.
This year marked the first annual decline for the main bourse since 2011.
South Korean markets will reopen on Friday.
Asian shares traded lower as political uncertainty in Greece and a sell-off in commodities weighed on investors' appetite.