The US Coast Guard said the Australian Safety Maritime Authority - which coordinated the helicopter rescue from the Akademik Shokalskiy - as well as the Russian and Chinese governments had requested assistance with the trapped ships.
Their Polar Star vessel, which was carrying out a port call in Sydney when assistance was requested, was on its way to refuel the US Antarctic Programs McMurdo Station on Ross Island.
It had planned to create a channel through the sea ice of McMurdo Sound for the annual resupply mission.
"The Polar Star will continue on this mission after conclusion of the vessel assistance mission," the US Coast Guard said.
The ship, which measures 122m in length, had recently undergone a $90 million overhaul over a three-year period.
It is able to break ice over 6m thick and can continuously break ice up to 1.8m while travelling at 3 knots.
The scientific team on board the Akademik Shokalskiy, led by scientists from the University of New South Wales, had been recreating Australian explorer Douglas Mawson's 1911 to 1913 voyage to Antarctica when they became stuck.
The six New Zealanders on the voyage - who are now on the Aurora Australis - are ornithologist Kerry-Jayne Wilson, University of Auckland doctoral student Colin Tan, historians John and Barbara Tucker, and two chefs.