"We discussed with Mr Rutte the last European Council in a very pragmatic way, and perhaps with a common vision on the fact that the migratory question must be addressed, starting from the defence of external borders and the fight against the traffickers, an issue which, as far as Italy is concerned, has become all the more significant after the tragedy of Cutro," Meloni said.
At least 72 migrants died in the disaster after their boat broke up in rough seas off the Calabrian coast.
She said the next EU summit must make progress on migrants starting with the central Mediterranean route and cooperation with African countries.
Meloni added that in the upcoming reform of the EU's Stability and Growth Pact, there must be a balance between stability and growth.
"In the Stability and Growth Pact there must be more consideration for the issue of balance between stability and growth, both are necessary," she told the press conference.
The Italian government has pinned the blame for the disaster squarely on the traffickers, who allegedly dodged tax police boat controls and made coast guard intervention impossible and then abruptly turned off Cutro causing the boat to break up.
"Migrations require an efficient European approach," Rutte told the press conference after meeting with Meloni.
"Last week's terrible shipwreck with dozens of people drowned highlighted more greatly the urgency of preventing this kind of tragedy, of making a united fight against the human traffickers.
"We must demolish this inhumane business.
"We must harmonise visa policy and be more present in Africa. We want to see what we can do to reach accords."
Rutte also said that he was not concerned about Italy's high public debt, the second highest in the eurozone after Greece's.
"The European Commission is charged with this and I am very struck by what Italy is doing in enacting the reforms" of the EU-funded post-COVID National Recovery and resilience Plan (NRRP), he told reporters.
"Italy has committed itself to making reforms and it is implementing them step by step."
ANSA