"Human lives must be saved, but in terms of legality and security", Toninelli said on Twitter.
Malta responded that it would "act according to the laws and applicable conventions", without further explanation.
Lifeline, operated by a German aid group, said it conducted the rescue in global waters, and asked for a safe port but was not told where they could land.
After turning away the Aquarius, which later docked in Spain, Rome vowed Saturday to block the Lifeline.
More than 640,000 migrants have arrived in Italy since 2014, many of whom made their way northward to join family or to countries perceived as providing more assistance until Italy's neighbours enacted stricter border controls.
Data from the German interior ministry does indicate that the proportion of crimes committed by foreigners has gone up in the past five years, but this can not be attributed specifically to migrant arrivals.
Matteo Salvini said the ship operated by the German aid group Mission Lifeline had loaded the migrants in Libyan waters after the Italian coast guard told it to leave the rescues to the Libyan coast guard.
Salvini has demanded that Malta, the EU's smallest country, allow the Lifeline to dock because it was in the island's waters.
Mission Lifeline said Friday that it still has not been assigned a port, despite its requests.
Senegal, Japan: underdogs aiming for a round of 16 spot
In their final group games on Thursday, Senegal will face Colombia in Samara while Japan plays Poland in Volgograd. Panama , one of the weakest teams in the field from the ultra-weak CONCACAF region is just happy to have qualified.
Return of US Korean War Vets' Remains Draws Nearer
At a Cabinet meeting at the White House, Mr Trump said: "They've stopped the sending of missiles, including ballistic missiles". US officials are looking for signs that North Korea intends to follow through with its stated desire to denuclearize.
USA withdraws from UN Human Rights Council in major support to Israel
United Nations officials privately confirmed they were expecting the U.S. decision to quit the rights body. The US is expected to announce its withdrawal from the United Nations Human Rights Council within hours.
The U.N.'s refugee agency says around 80,000 people are expected to arrive by sea this year, about half the number from 2017.
The comments came after Italy's government recently refused to allow the Aqurius, another rescue ship carrying more than 600 migrants, to land at Italian ports.
Both leaders are hardliners on immigration issues.
German Chancellor Angela Merkel and German Interior minister Horst Seehofer attend an event to commemorate victims of displacement in Berlin, Germany, June 20 2018.
During her visit to Beirut, Mrs Merkel will hold several meetings with prime minister-designate Saad Hariri who has been corralling much of the global support for Lebanon.
But it now also takes issue with an agreement announced Tuesday by Merkel and French President Emmanuel Macron to set up a common budget for the eurozone which will fund investments in poorer member states.
Germany and eight other European Union members say euro zone banks must first reduce exposure to risks before the project can start.
After her meeting with King Abdullah, Merkel is slated to meet German military personnel who are now stationed in Jordan as part of a US -led coalition tasked with fighting the Daesh terrorist group.
"The overwhelming majority of the German population supports this idea and this concept, and that's why we want to provide support today (yesterday) for implementing it", he said.
The stand-off has led to speculation that Merkel's conservative bloc - composed of her Christian Democratic Union (CDU) and its Bavarian counterpart, the Christian Social Union (CSU) - could split in two, thereby robbing her of her parliamentary majority and perhaps even forcing snap elections.