Chris Turney, one of the leaders of the scientific expedition, said via Skype from the stranded ship that those on board were in good spirits and wanted their families and friends to know they were safe and well.
"It's Antarctica, we are just taking it one day at a time," he told AFP.
"The conditions are so extreme in Antarctica, you just never know. We are always hopeful."
In a brief video posted on his Twitter account shortly after 1830 GMT, Turney seemed optimistic that the weather was getting better and that a ship rescue could still be viable.
"A disappointing day but hopefully the icebreakers will get in tomorrow," he said.
He added: "Good news: Visibility improved to horizon. Wind moderate (20 knots)."
Turney, who is professor of climate change at the University of New South Wales in Sydney, said satellite images indicated that their vessel had become stuck in ice which had broken away from a glacier.
The fierce winds had pushed it into an area of normally open sea, blocking the ship's progress, and this ice was now three to four metres thick in some places, although in others there were gaps with no ice.
"It's an unusual event that's happened," he said. "We were in the wrong place at the wrong time."
Turney had earlier tweeted that cracks were developing in the ice around the bow of the ship, something he hoped would help free the vessel.
The team onboard has been carrying out the same scientific experiments which Mawson's group conducted during the 1911-1914 expedition in the hope they could help in climate change research.
Several members of the team have already battled sea ice to reach the historic Mawson's Huts -- built and occupied by the 1911-1914 expedition -- which have been isolated for years by a giant iceberg.