RCCNZ said the Janas was likely to accompany the Antarctic Chieftain for about two days as its performance in open water was assessed.
The Antarctic Chieftain was currently travelling at a speed of about 7 knots (13km/h) and could take up to two weeks to reach Nelson, almost 4500km away.
RCCNZ rescue mission coordinator Dave Wilson said the operation to free the vessel from the ice had been challenging.
"The crew of the Polar Star and the US Coast Guard have done an outstanding job and we'd like to thank them all for their efforts.
"They've worked around-the-clock in extreme conditions to bring the Antarctic Chieftain to safer waters.
"We'd also like to thank the captain and crew of the Janas for making themselves available to provide assistance."
The Antarctic Chieftain became stuck about 1700km from McMurdo Sound, on the edge of New Zealand's search and rescue region. Half of its crew of 26 are New Zealanders.