The New Zealand share market rose 10 points to close at 3367 on low turnover of $4 million on Tuesday.
At the close, Telecom was up up 5 cents to $3.28, while fellow market heavyweight Fletcher Building rose 9c to $7.29.
Contact Energy was up 12c to $8.48, while The Warehouse gained 3c to $3.40.
Auckland Airport rose 1c to $2.12, while Air New Zealand climbed 6c to $1.18.
Telstra Clear dropped 5c to $5.25.
Australian market weaker
The Australian share market has closed slightly on Tuesday weaker despite a cut to official interest rates and a drop in the oil price as concerns about Hurricane Gustav were alleviated.
At 1615 AEST the benchmark S&P/ASX200 was down 2.3 points, or 0.04%, to 5,116, while the broader All Ordinaries fell five points, or 0.1%, to 5,195.
The September share price index futures contract was down five points to 5,135 on volume of 24,331 contracts.
Oil prices dived to four-month lows overnight, sliding below $US110 in London as a weakening Hurricane Gustav reduced the threat of damage to oil and gas platforms in the Gulf of Mexico.
At 1636 AEST, spot gold in Sydney was trading at $US809.50 an ounce, down $US23.30 on Monday's local close of $US832.80.
Wall Street did not trade on Monday due to the Labor Day holiday in the United States. It finished on Friday with the Dow Jones industrial index down 171.63, or 1.47%, to 11,543.55.
Japanese shares fall as PM resigns
In Japan, share prices fell1.75% by the close, hit by a stronger yen and political uncertainty following Prime Minister Yasuo Fukuda's abrupt resignation, dealers said.
The Tokyo Stock Exchange's benchmark Nikkei-225 index fell 224.71 points to end at 12,609.47.
The broader Topix index of all first-section shares declined 18.27 points or 1.48% to 1,212.37.
Mr Fukuda's surprise announcement on Monday came after the 72-year-old political moderate failed to reverse a slump in his popularity despite reshuffling his cabinet and unveiling a major economic stimulus package.