After continued stormy weather, seas off the Tuscan Island of Giglio were calm enough on Sunday to resume the work.
However, the Italian government said winds were increasing and that the work would be halted before seas become too choppy.
The search of the half-submerged vessel for the bodies of the 15 people missing in the Jan. 13 capsizing was suspended due to the sea conditions.
At least 17 people died after the cruise ship rammed a reef off Giglio and flipped over on its side. Rough seas so far have thwarted efforts to pump out the fuel to avoid pollution of pristine waters.
See photos of the cruise ship Costa Concordia off the coast of Italy.
The Associated Press contributed to this story.
