Anti-government demonstrators continue to blockade the Suvarnabhumi and Don Muang airports.

Some international flights have been allowed to depart airports in Phuket, Chiang Mai and the military airport in Utapao.

They included Thai Airways flights to Sydney, which have been heavily booked.

The Department of Foreign Affairs and Trade says Qantas will have an extra flight back to Australia departing Phuket late on Monday.

The Airbus will carry Qantas passengers as well as Australians booked with other carriers.

The department has urged Australians not go to airports unless they have confirmed flights.

Acting Foreign Affairs Minister Simon Crean says Australian authorities are continuing to negotiate more flights with their Thai counterparts.

"We are making every effort to use alternate approaches, not just the Phuket option, but also Utapao airport ... (and) Chang Mai," Mr Crean told ABC Television.

He said the government was very "frustrated" with Thai airport authorities.