At least 70 people died in the tragedy.
"The Holy Father's words are a big call to all the institutions," Meloni said on Facebook.
"We are doing our part as the government, continuing to use all the efforts necessary to combat human traffickers and stop the deaths at sea".
The pope said during his Angelus service on Sunday that human traffickers must be stopped, and expressed his sadness at the disaster off the Calabrian town of Cutro.
"May human traffickers be stopped, and may they not continue to throw away the lives of so many innocent people," the Argentine pontiff said.
"May the clear waters of the Mediterranean Sea never again be bloodied by such dramatic incidents."
The pope also expressed "appreciation and gratitude to local residents and institutions for their solidarity and welcome for these brothers and sisters of ours".
He asked God to give everyone the "strength to understand and mourn."
Italian magistrates union ANM, meanwhile, said on Sunday that it is impossible to ban refugees from fleeing wars and other life-threatening situations.
Interior Minister Matteo Piantedosi had faced calls to quit after saying asylum seekers should not put their children's lives at risk with risky crossings, arguing "desperation" was no justification.
"No law could ever oblige someone not to flee countries where war or poverty impede access to dignified life conditions," the ANM said in a document.
"Therefore, the ANM hopes that the obligation to rescue (people in distress), which is engraved in our Constitution as well as in the international conventions, is always respected."
A probe has been opened into whether rescue operations were negligently delayed.
The government has staunchly defended the coast guard, which has said it followed its rules in handling such situations.
Meloni on Saturday dismissed speculation that her government may have in some way impeded operations that would have saved the victims of the disaster.
ANSA
