The boat's sinking last April left as many as 800 people dead in the worst maritime tragedy in the Mediterranean since World War II.
Italian Prime Minister Matteo Renzi has vowed to give all of the victims decent burials and the delicate and complex task of lifting the vessel from the seabed at a depth of 380 metres (1,245 feet) got under way on Wednesday.
But weather conditions have deteriorated since then and the navy said the operation had to be suspended.
"Recovery activity will resume in the coming days when the weather conditions allow it progress while ensuring the safety of personnel and equipment," a navy statement said.
The stricken trawler sunk in pitch darkness after colliding with a Portuguese merchant ship that had gone to its aid.
There were only 28 survivors and they estimated that around 800 people had been crowded on board when it left Italy.
Fifty bodies were recovered after the accident and another 171 since then from around the wreck, suggesting as many as 600 corpses could be brought up with the boat.
After it reaches the surface, the wreck is to be taken by barge to Sicily, where forensic experts are on standby to begin trying to identify the bodies.
Around 9,000 people are known to have lost their lives in the Mediterranean since the current migrant crisis erupted in mid-2013.
Aid agencies say it is likely many more disappeared without a trace after being abandoned on the high seas by traffickers.