Victorian authorities have urged tourists and locals to leave the state's alpine and East Gippsland regions on Thursday.

In NSW, people near Batlow have been asked to leave on Thursday while holiday-makers in the alps and between Nowra and the Victorian border should be out by Friday afternoon.

While supplies are high in most communities, fuel has been restricted at some sites to guarantee that enough remains for firefighters.

Restocking tanks is also an issue, with emergency services due to escort petrol tankers into Moruya on Thursday night.

A 50-litre limit per person was imposed at one Moruya petrol station when it faced running dry within hours with a line stretching more than a kilometre.

Drivers had already bought 55,000 litres in half a day of trade - double January's daily average.

Further south, some sites at Merimbula, Bairnsdale and Lakes Entrance have run out of either petrol or diesel.

Deliveries have been made to key centres Batemans Bay and Eden, where demand remains high.

Caltex said it was doing what it could to deliver more fuel to bushfire-affected areas.

"We thank our customers for their patience as we manage the increased demand at this difficult time," Caltex spokesman Richard Baker said in a statement.

NSW Premier Gladys Berejiklian on Thursday said she was relieved some towns had power and other services restored.

"We encourage people to exercise caution (driving out)," she told reporters on Thursday.

"We do appreciate that for some, it is difficult to access supplies but it's much easier than what it was yesterday and the day before."

More than 18,000 homes and businesses remain without power in bushfire-affected NSW and Victorian communities.

Australian Associated Press