The benchmark S&P/ASX 200 reversed early gains and is down 0.6% in Sydney.
Mr Turnbull has been trying to pass through labour reform bills but has faced hostility to it from the senate.
As a result, he's threatened to dissolve both houses of parliament and call an early election on 2 July.
Polls indicate his party are likely to win, even though Mr Turnbull's approval ratings have recently fallen.
Asian stocks overall are trading mixed with markets in New Zealand, South Korea and Singapore in negative territory.
Japan's financial markets are closed for a public holiday.
In China, Hong Kong's Hang Seng opened 0.2% higher while the Shanghai Composite also rose, increasing 1.7%.
However mainland investors may trade cautiously after China's central bank governor warned over the weekend that the country's corporate debt levels were too high and that more reforms in its capital markets were needed.
People's Bank of China (PBOC) governor Zhou Xiaochuan said in a speech at the China Development Forum conference that lending as a ratio to gross domestic product "is too high".
Analysts said the admission from the PBOC could dampen investors' risk appetite.
This week the "market mood, rather than data, will rule the roost in Asia," Vishnu Varathan from Mizuho Bank said.
Australian stocks have fallen after Prime Minister Malcolm Turnbull recalled parliament and brought the budget forward, setting the scene for an early election.