The decision was made as a result of protests by the victims’ families, who had been speaking out against the transfer since Wednesday morning.
However, some families have given their consent, with 14 coffins having already departed on Wednesday evening.
Another 10 will perhaps leave Thursday.
The 17 bodies of the victims for whom the families have decided to transfer to Afghanistan will remain in Crotone until bureaucratic problems have been resolved.
The initial decision by the Interior Ministry came as a surprise to the relatives of the victims, creating the catalyst for the protests.
The local authorities in Crotone have reportedly already allocated funds for repatriation.
Interior Ministry sources later said the planned transfer was a "temporary and not permanent" solution "to give immediate dignity" to the dead.
"It is not easy to proceed with immediate repatriation to Afghanistan," the ministry said, in reference to the fact that most victims were Afghani.
Italy will in any case "proceed on the basis of the requests of each family," the government source continued.
"If repatriation of the body is required, the Italian state will carry all the costs."
"The Italian government is playing with the dead," read the placard of one Afghan woman who lost her daughter and son-in-law in the shipwreck.
She was protesting outside the makeshift chapel of rest, a sports arena, in Crotone on Wednesday.
"They have tried to remove the coffins without saying anything first," another Afghan national said.
Seventy-two people have been confirmed dead from the Lampedusa disaster, with 80 known survivors.
Around 30 more are believed to be missing, feared drowned.
ANSA