The vessels are among about 50 ships stuck firm in the thick ice in the Baltic around Sweden, the Stockholm archipelago and the Finnish island of Aland.
Rescuers from the Swedish Maritime Administration and ice-breaking vessels are trying to reach the stricken ships but are being hampered by gale-force winds.
Peter Lindquist, spokesman for the rescuers, said: "As soon as they break the ice, it freezes over again."
He added there were no immediate plans to bring people off the ships, but helicopters and military hovercraft were on standby in case evacuations would become necessary.
The agency said the ships were the Amorella, a passenger ferry with 943 people on board, the smaller Via Mare ferry carrying 66 people, the roll-on-roll-off ferry Sea Wind with 32 people and the Regal Star, a cargo ship with 56 people on board.
Two other ferries that got stuck in the ice were able to break free earlier.
"It has been a lot colder than normal in the southern parts of the Baltic sea, but in the north all is normal with normal levels of ice," Tommy Gardebring of the Maritime Search and Rescue Centre in Gothenburg said.
"However, in the worst-affected areas, the ice breakers that normally operate haven't been able to cope with the ice, which is why we are sending additional ice-breakers."