The market stayed in positive territory for much of the day but retreated after the Wall Street Journal said concern was mounting that Lisbon will struggle to refinance billions of dollars in debt due in 2013.
At the close, the benchmark S&P/ASX 200 was 0.02 percent, or 0.9 points, lower at 4,224.2.
"Equity markets pushed higher early in the session, but pulled back as fears mount that Portugal will need a second bailout," said IG Markets' Stan Shamu.
"Reports are suggesting that Portugal won't be able to return to markets for financing next year."
Investors were also cautious ahead of a conclusion to Greek debt talks and lacked leads as many Asian markets were closed for the Lunar New Year holiday.
In Wellington, the benchmark NZX 50 fell 16.82 points, or 0.52 percent, to 3,210.64, ending a six-day winning streak as profit-takers locked in gains.
Markets in Hong Kong, Singapore, Seoul, Kuala Lumpur, Shanghai and Taipei were all closed on Tuesday for the public holiday.
The Australian dollar was fetching 104.92 US cents late in the day, up marginally from 104.86 US cents on Monday.