The benchmark S&P/ASX 200 index closed up 11.6 points to 4,635.2 in thin trade. Though trading near a 17-month peak, the index remains 30 percent below its all-time high. New Zealand's benchmark NZX 50 index reversed early losses to end up 3.1 points at 4,057.8. Monday's session was shortened ahead of the two-day Christmas holiday. Trading is set to resume on Thursday.
"Assuming a solution is ultimately found, which we think it will be, then share markets are likely to have a good year ahead," said AMP Capital Markets head of investment strategy Shane Oliver. He said he expects the local benchmark index to reach 5,000 by the end of 2013.
"Shares remain cheap particularly relative to bonds and cash and Australian shares are being given an added impetus by lower Reserve Bank interest rates, which should help boost profit growth," Oliver said. Most economists expect the central bank to continue cutting interest rates in the new year. Miner BHP Billiton gained 0.4 percent as iron ore prices remained strong, while defensives also drew favour. Phone company Telstra gained 0.7 percent.
Shares in surfwear company Billabong International initially rose 3.6 percent after the take-over target said it had allowed the backers of a $556 million buyout offer to examine its books. Its shares ended up 0.6 percent at A$0.83, still well below the A$1.10 per share offer price. Department store Myer gained 1.0 percent to A$2.07 on hopes of strong holiday sales. The Australian Retailers Association predicts Christmas sales will be up a solid 3.9 percent on last year.