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.

Brace will take on an as yet unnamed opponent for the vacant WBC International bantamweight title.
The 26-year-old has won all five of her professional bouts so far.
Brace quit amateur boxing after being told she was ineligible to compete at the 2014 Commonwealth Games because of suggestions she had fought professionally as a kickboxer.
Her involvement at the 2013 Unified Kickboxing World Championships ruled her out of the Games in Glasgow, an amateur-only event.
Find out how to get into boxing with our special guide.

Alexandra North, 25, a zoology graduate from Swindon, beat about 150 applicants to land the £24,000-a-year role with Suffolk Wildlife Trust.
She will start work as Ipswich's dedicated hedgehog officer next month.
The trust chose to focus on the town after receiving a large number of sightings by members of the public.
Almost 12,000 hedgehogs, dead and alive, have been recorded in Suffolk over the past two years, with about 2,500 of these around Ipswich.
The trust previously said there was a "rich natural network" for hedgehogs across Ipswich, "including its beautiful parks as well as the cemetery, allotments and churches".
Ms North, who currently works as a researcher at Cambridge-based conservation group Birdlife International, saw off competitors from countries including France, Spain, Germany, South Korea, China, the US and Nepal.
The job advert for the two-year role was shared around the world and mistakenly touted as a £2.4m post in the Taiwanese press.
However, in the end the wildlife trust interviewed just four candidates, all of whom were from the UK, "because they matched the criteria most closely, not because they were based in the UK", a trust spokeswoman said.
"The competition was tough. We had applications from around the world and some really strong candidates," the trust said.
Ms North said she was "really excited by the prospect of a great project with the overall aim to make Ipswich a really hedgehog-friendly town".
Her work will involve building a network of volunteers who in turn will help build a network of hedgehog-friendly routes around Ipswich's urban landscape.
Ms North, who boasts a postgraduate degree in biodiversity and conservation, said: "Everyone loves hedgehogs and they are so important to the biodiversity of our landscape and our wildlife.
"I really hope I can engage with people and encourage everyone to see how making small changes really can make a difference to these little creatures."
Asian shares traded lower as political uncertainty in Greece and a sell-off in commodities weighed on investors' appetite.
[NEXT_CONCEPT]
Welsh boxer Ashley Brace will fight for her first professional title in her hometown of Ebbw Vale on 22 April.
[NEXT_CONCEPT]
A hedgehog officer is set to start work to improve animal numbers after an advert for the job sparked worldwide interest.