In South Korea, the Kospi closed down 0.19 percent or 3.85 points, at 2,038.39, while Hong Kong's Hang Seng fell 0.76 percent by mid-afternoon.
Chinese markets were mixed, with the Shanghai composite closed down 0.15 percent, or 4.55 points, at 3,118.43 while the Shenzhen composite finished down 0.378 percent or 7.53 points at 1,984.1.
China's efforts to cool the property market appear to be coming through, with November new home prices up 0.6 percent from the previous month, slowing from October's 1.1 percent increase.
China's largest property developer China Vanke fell to a four month low, down 6.06 percent to 21.10 yuan per share. The Shenzhen-listed company said on Sunday it would terminate a key deal to acquire a property development arm of Shenzhen Metro Group after failing to get approval from some shareholders, Reuters reported.
Markets also picked up on South Sea tensions after a Chinese warship seized last week a U.S. underwater drone in the South China Sea, which triggered a formal diplomatic protest and a demand for its return last Friday. The political fallout continued over the weekend even after Beijing agreed to return the drone, with U.S. President-elect Donald Trump taking jabs at China on Twitter.
"This incident is a reminder to markets that geopolitical tensions may deserve more risk premium under the Trump administration," said Ric Spooner, chief market analyst at CMC Markets, in a note on Monday.
Investors will also eye the Bank of Japan's two-day monetary policy meeting starting on Monday and Hong Kong's November unemployment rate.