SYDNEY, June 23 (Reuters) - Passengers on two flights between Australia and New Zealand have been ordered to immediately isolate and undergo COVID-19 testing after authorities traced a traveller who tested positive in Sydney after visiting Wellington.

The case, which adds to a growing coronavirus outbreak in Sydney, prompted New Zealand authorities to suspend quarantine-free travel to and from New South Wales state for three days from midnight on Tuesday (Jun 22).

The Qantas flight to Wellington on Friday and the Air New Zealand flight to Sydney on Monday were added to a list of virus "hot spots" drawn up by Australian authorities.

The list has been growing with 21 infections detected over the past six days in New South Wales, Australia's most populous state.

Masks have been made mandatory at all indoor locations in state capital Sydney in a bid to contain the Delta variant, which has been classified by the World Health Organization as among the four COVID-19 variants of concern.

The traveller case has also prompted New Zealand health officials to consider a lockdown in Wellington, with authorities saying the person likely visited several popular tourist locations in the city.

New Zealand and Australia opened up a so-called "travel bubble" in April. There have been periodic, targeted suspensions since then due to small outbreaks in Australia.

Snap lockdowns, tough social distancing rules and swift contact tracing have helped both Australia and New Zealand to contain outbreaks and keep their COVID-19 numbers relatively low.

New Zealand reported its last locally acquired case in February while Australia has had sporadic outbreaks.

Australia has reported just over 30,350 cases and 910 deaths since the pandemic began, while New Zealand recorded more than 2,300 confirmed cases and 26 deaths.