The icebreakers Krasin and Admiral Makarov neared the trapped Bereg Nadezdy at 5 a.m. Moscow time, RIA Novosti reported.
After 4 1/2 hours, they began towing it toward its mother fishing ship, the Sodruzhestvo, five miles away.
The Bereg Nadezhdy, the Professor Kizevetter research vessel and the Sodruzhestvo, with more than 400 people aboard combined, got trapped in 6-feet-thick ice on New Year's Eve. Two other ships, the Mys Yelizavety and the Anton Gurin, got stuck three days later.
On Jan. 7 and 8, the Admiral Makarov freed the Professor Kizevetter and the Mys Yelizavety, while the Anton Gurin broke free on its own power.
High winds, low visibility and shifting ice floes have slowed the rescue, the ministry said.
The icebreakers plan to move the ship toward open water in a single-file convoy.