In a separate report, Deutsche Welle (DW), Germany's worldwide broadcaster, noted that Italy's ruling, centre-left Democratic party has come under pressure over the migrant issue. The country's representative to the EU, Maurizio Massari on Wednesday (28 June) warned in a letter to the bloc that the situation had become "unsustainable".
About 10,000 people have been rescued over the past three days, mainly from unsafe smugglers' dinghies that had set out from Libya. More than 500,000 migrants have arrived by boat in Italy since 2014.
About 2000 have died or are missing feared drowned, the UN's refugee agency said.
Volunteers and Guardia Civil officers help injured migrants to disembark from the Spanish Guardia Civil Rio Segura Patrol Ship with 1,216 migrants onboard including 256 children and 11 pregnant women, who were rescued in the Mediterranean sea on June 29, 2017.
It is a gateway to Europe for travellers from across sub-Saharan Africa and also from the Arabian peninsula, Egypt, Syria and Bangladesh.
This young girl was rescued by NGO Proactiva Open Arms about 20 nautical miles off the coast of Libya in October 2016.
If Italy goes ahead with its threat, EU Frontex operations would not be up for discussion since they are governed by global law.
Italy made a formal request for more support from the European Union on Wednesday as it copes with an increase in migrant rescues, including a reported proposal to limit the types of ships that can offload migrants in Italian ports.
"Italy has reached saturation point", he said, adding that Rome had planned for 200,000 beds for asylum-seekers and those were nearly all taken. The suggestion has widely been reported in Italian media.
The surge in migrants this week prompted Italy's interior minister, Marco Minniti, to cancel a trip to Washington to address the growing humanitarian crisis, which is quickly morphing into a political one for the country's left-leaning coalition government.
After meeting Ambassador Massari on Wednesday, EU migration commissioner Avramopoulos praised Italy's exemplary behavior to date and agreed: "Italy is right that the situation is untenable".