The Snow Dragon icebreaker was itself stalled by heavy ice, officials say.
It had been trying to cut a path through the ice in order to help the research vessel reach open water.
The Akademik Shokalskiy, which has been trapped since Christmas Day, has 74 on board and is being used by the Australasian Antarctic Expedition.
They are following the route explorer Douglas Mawson travelled a century ago.
One of the leaders of the expedition, Chris Turney, earlier tweeted an image of the Snow Dragon icebreaker – also known as the Xue Long – on the horizon as it approached the research ship.
The Chinese vessel came within seven nautical miles of the expedition ship, but encountered heavy ice and was forced to return to the open sea.
“Our rescue boat, the Xue Long, has had to turn back because the ice was too thick for it to get through,” said Alok Jha, a journalist on board the Shokalskiy.
The Australian Maritime Safety Authority, which is coordinating the rescue, confirmed that a French vessel had also failed to penetrate the ice.
The agency said another boat, the Aurora Australis, was on its way to the Russian vessel and expected to arrive on Sunday.
“I think we’re probably looking at another 24 hours of twiddling our fingers and waiting for something to happen,” the expedition’s spokesman Alvin Stone told the Associated Press.
Correspondents say expedition members could be winched to safety by a helicopter if the weather remains favorable.
The research ship Shokalskiy was trapped by thick sheets of ice that were driven by strong winds about 1,500 nautical miles south of Hobart – the capital of the Australian state of Tasmania.
There had also been fears that blizzards could hamper the rescue effort.
The Shokalskiy is well stocked with food and is in no danger, according to the team.
Although trapped for the moment, the scientists are continuing their experiments. They have been measuring temperature and salinity through cracks in the surrounding ice.
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