An Australian icebreaker trying to reach the Russian scientific mission ship was forced to turn back.
Earlier attempts by Chinese and French icebreakers to reach the Akademik Shokalskiy were also foiled by the thick ice.
Seventy-four scientists, tourists and crew are on the ship.
The vessel is being used by the Australasian Antarctic Expedition to follow the route explorer Douglas Mawson travelled a century ago.
Scientists on board thought the ice was much thicker than usual for this time of year.
The Aurora Australis icebreaker had been forced to turn back to clear water and was repositioning to try to find another route towards the Shokalskiy.
In a statement, the Australian Maritime Safety Authority (AMSA) said: “The area where the MV Akademik Shokalskiy is beset by ice is currently experiencing winds of up to 30 knots and snow showers.”
“These weather conditions have resulted in poor visibility and made it difficult and unsafe for the Aurora Australis to continue today’s attempt to assist the MV Akademik Shokalskiy.”
Earlier, it was thought that passengers could be winched to safety by a helicopter on board the Chinese icebreaker, which had to abort its rescue mission on Saturday.
However, AMSA spokeswoman Lisa Martin told Reuters news agency: “We can’t fly a helicopter in these conditions either. There is essentially nothing we can do at this point of time.”
The Aurora Australis would have to wait for the weather to improve before making a second rescue attempt, she added.
Despite being trapped, the scientists on board have continued their experiments, measuring temperature and salinity through cracks in the surrounding ice.
Akademik Shokalskiy was trapped on Christmas Day by thick sheets of ice, driven by strong winds, about 1,500 nautical miles south of Hobart – the capital of the Australian state of Tasmania.
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