Flights in and out of Melbourne and Avalon will resume this afternoon.
In a statement, the budget airline said the safety of passengers and crew is its number one priority.
"Jetstar will not be flying into airspace that remains affected by the ash cloud until we are confident that it is safe to do so," the statement read.
Jetstar and Qantas, which follow the same safety policy, yesterday cancelled all trans-Tasman and domestic flights - about 50 in total.
Both airlines also extended their no-fly policy to some Singapore and Los Angeles services. Some incoming flights from Chile were put on hold.
Pacific Blue cancelled six flights, while Air New Zealand and Emirates kept flying but at a lower altitude than usual.
Among those stuck in New Zealand were several sports teams.
The Australian netball side were due to return home yesterday morning but their Qantas flight was delayed until tonight.
The delay means players will have fewer days to rest before they leave for pre-tournament preparations for the World Netball Championships next month.
It also means that defender Susan Fuhrmann - who has been studying whenever possible on tour - will return to Perth with only hours to spare before a pharmaceutical exam.
The West Tigers rugby league team, from Sydney, were stranded at their hotel after their match against the Warriors in Auckland on Sunday when their Qantas flight was cancelled.
Spokesman Wayne Cousins said the timing could have been unlucky if Tigers players had have been involved in the State of Origin match tomorrow night.
However, none was chosen for the series.
Most stranded passengers at Auckland Airport were philosophical about the cause of the delays, but were frustrated by what they said was poor communication.
Victoria Walker, whose flight home to Sydney was cancelled, said she felt abandoned by Qantas.
"I was on hold to [the information line] for two hours and 40 minutes before I switched it off and decided to come to the airport."
Masterton resident Belinda Goodwin's Pacific Blue flight to Rarotonga reached the end of the runway but turned around at the last minute.
After being put up for the night by the airline, she has decided to abandon her holiday, switching airlines yesterday to return home to Wellington.
With flights until Thursday full or quickly filling, many passengers were facing a long wait to get home.
Jetstar passengers Anthony and Elaine Smuts were delighted to be put in four-star accommodation by the aiRline, but did not expect to get away for three days.
Mr Smuts was considering whether to hire a campervan and drive home to Christchurch "or sit in a hotel room for another two days doing nothing".
WAITING FOR CLEAR AIR
Number of passengers affected in NZ domestic and transtasman flights (Sun-Mon): About 18,000
JETSTAR
74 flights cancelled, 10,000
passengers affected.
QANTAS
62 flights cancelled, about 5500
passengers affected.
PACIFIC BLUE
6 flights cancelled, about 500
passengers affected.
VIRGIN
11 flights cancelled, about 700
passengers affected.
EMIRATES
2 flights cancelled, about 150
passengers affected.
AIR NEW ZEALAND
No flights cancelled.