"The Gregoretti berthed in the port of Augusta overnight, as is normal procedure for a military vessel. Now the EU has to act because the migration question concerns the whole continent," Transport Minister Danilo Toninelli said in a statement.
Some 140 migrants, who had set off from Libya in two rickety boats, were picked up by Italian patrols on Thursday night and transferred to the Gregoretti ship.
The operation took place on the same day that at least 115 other migrants were believed to have drowned in a shipwreck off Libya -- the Mediterranean's deadliest tragedy this year, according to the International Organization for Migration (IOM).
Several migrants aboard the Gregoretti have already been evacuated for medical attention, including a seven-month pregnant woman, her two children and her partner.
However, Italy's far-right Interior Minister Matteo Salvini has reiterated that the remaining migrants would not be able to leave the vessel until other European countries agree to take them in.
Salvini, also deputy prime minister, has taken a hard line against migrants rescued at sea being brought to Italy, which he says bears an unfair burden in the crisis.
French President Emmanuel Macron announced last Monday that 14 EU members had approved a plan to redistribute refugees rescued in the Mediterranean, and eight said they would actively take part.
The proposal drew Salvini's ire because it still involved allowing migrants to disembark on his country's territory.
He said the agreement underscored a demand that Italy "continue to be the refugee camp of Europe".
Pope Francis on Sunday called on the international community to "act swiftly" to help avoid further deaths.
"I have learned with sorrow the news of the dramatic shipwreck that happened in recent days in the Mediterranean where dozens of migrants including women and children have lost their lives," he said Sunday during his weekly Angelus address on St Peter's Square.
"I am renewing my call that the international community act swiftly and decisively to avoid that such tragedies repeat themselves and guarantee the safety and dignity of all."