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The first ship, the Blue Sky M, was spotted floating adrift near the coast of Corfu on Tuesday
The Italian coast guard says a merchant ship with at least 400 migrants on board is heading for the Italian coast.
The Ezadeen, sailing under the flag of Sierra Leone, has no crew on board and has lost power in rough seas off the south-east of Italy.
The Icelandic coast guard confirmed to the BBC that one of its vessels was assisting in efforts to board the ship.
Almost 1,000 migrants were rescued from another ship found abandoned without any crew earlier in the week.
The Icelandic coast guard told the BBC that high seas and bad weather were making it difficult to board the 73-metre (240ft) Ezadeen, which is 65km (40 miles) off the south-eastern tip of Italy.
The Icelandic coast guard vessel Tyr is patrolling off the Italian coast as part of the EU Frontex border control mission.
The alarm was raised in a distress call from one of the migrants who managed to operate the maritime radio on board the Ezadeen, according to the Italian coast guard: “We’re without crew, we’re heading toward the Italian coast and we have no-one to steer.”
The Ezadeen was built nearly 50 years ago and is a livestock carrier.
It was due to be sailing between Cyprus and the southern French port of Sete, according to a website tracking maritime movements.
It appears to be registered to a Lebanese company and has come under the control of human traffickers.
Analysis: Jonathan Josephs, BBC News
The Ezadeen is just the latest uncrewed ship full of would-be migrants to be left to drift to its fate in the Mediterranean Sea.
One of the ships which has gone to its rescue, the Icelandic Coastguard’s ICGV Tyr, has been involved in four other similar rescues since it was deployed to the area at the beginning of December.
People traffickers appear to be behind the phenomenon and one source with close knowledge of the rescue operations is concerned that it “seems to be something of a new trend”.
What’s changed is that Italy is no longer carrying out Operation Mare Nostrum, a €9m-a-month search-and-rescue response to the migrants in trouble around its coastline.
Since November the EU’s border agency Frontex has been conducting its Operation Triton over a very specific area and with limited resources.
MEP Claude Moraes chairs the Civil Liberties, Justice and Home Affairs Committee of the European Parliament and says “Triton scares no-one”.
He believes that because it doesn’t have the weight of a sovereign justice system behind it people traffickers are now less afraid to operate the smuggling routes.
They charge migrants thousands of dollars for the promise of a better life in Europe and show little concern for their welfare.
Mr Moraes wants EU member states to do more to help the migrants and clamp down on the traffickers.
That might help the new year see a reduction of the number of migrant deaths in the Mediterranean – there were more than 3,000 in 2014.
The first ship, the Blue Sky M, carrying 970 people, was abandoned and left on autopilot by its crew, believed to be people-traffickers.
Italian coast guards brought it under control and safely docked it at the Italian port of Gallipoli on Wednesday.
The migrants, believed to be mainly Syrians and Kurds, have been taken to local schools and a gymnasium.
Thirty-five of them were taken to hospital, with some treated for hypothermia, Italian Red Cross spokeswoman Mimma Antonacci said.
The Italian Red Cross had previously said that four people were found dead on the ship. It later withdrew its report, and officials now say no-one is known to have died on the ship, Reuters reports.
Migrant surge
Italy has had to deal with a massive surge in migrants – many of them from the Middle East and the Horn of Africa – setting off on boats with hopes of reaching Europe.
The Blue Sky is listed as a general cargo ship, sailing under a Moldovan flag.
The safety manager of a company hired to provide safety certification for the ship told the BBC he had withdrawn its certificate several months ago after finding it unsafe.
Those aboard the Blue Sky M made it to land, but the fate of those on the Ezadeen remains uncertain
Medics were on hand to treat migrants as they disembarked from the ship
Many of the migrants on the Blue Sky M are believed to have come from Syria
Greek officials were first alerted to the ship when it was near Corfu.
A man aboard is reported to have asked for food, water and blankets. The distress call to Greek emergency services prompted the navy to send a helicopter and a warship.
The Greek authorities had said no-one aboard the vessel was in danger.
The Blue Sky M was reportedly heading for the port of Rijeka in Croatia from Turkey.
According to tracking website MarineTraffic, the ship abruptly changed direction south of Othonoi on Tuesday morning, heading west towards Italy.
Weather conditions in the Ionian sea have been poor for several days, hampering the rescue of those on board the Norman Atlantic ferry which caught fire in the area, killing at least 10 people.
BBC