Crude for October delivery was trading up 79 cents at $118.94 a barrel by 0415 GMT, after settling up $1.88 on Wednesday. Oil has risen $3.56 in the past three sessions.
London Brent crude was up 85 cents at $117.07 a barrel.
Gustav is expected to hit the US Gulf Coast around Monday as the first major hurricane to threaten US energy installations there since Katrina and Rita in 2005, and about 85 per cent of US offshore oil and gas production could be in its path.
AccuWeather said Gustav could strengthen into a Category 4 or 5 storm over the Gulf -- home to a quarter of US crude oil production and 15 per cent of the nation's natural gas output.
Shell Oil Co, the US Gulf of Mexico's largest producer, said its oil production would be affected as early as Thursday as it evacuated all workers from offshore operations. Gustav could shut down 85 per cent of US production platforms in the Gulf, private forecaster Planalytics said.
"This is the time of the year that (hurricane) premiums can be put into the market, $10 to $15 a barrel," said Peter McGuire, managing director of Commodity Warrants Australia. "(There is the) Labour Day holiday on Monday, and the market will be shut. There's a lot of nervousness in the market."
McGuire said oil could hit around $130 over the next week and a half on hurricane worries. Oil was last at that level five weeks ago.
Analysts say US companies could be forced to draw on oil inventories to compensate for disruptions.
US government data showed an unexpected, 100,000 barrel drop in US crude inventories last week, against forecasts of a 1 million barrel rise.
Traders were also eyeing an OPEC meeting scheduled for Sept. 9 in Vienna as well as escalating tensions between Russia and the West after US President George W. Bush condemned Russia for recognising breakaway regions in Georgia.
Venezuelan President Hugo Chavez on Wednesday said oil prices were fair, and the nation's energy minister said OPEC should keep output steady or make cuts at its next meeting in September.