In a statement late Sunday after speaking with his Italian counterpart, Mr Muscat refused to let the ship dock in a Maltese port, but said Malta would conduct emergency medical evacuations if necessary. Passengers include 11 children and seven pregnant women, as well as 123 unaccompanied minors.
In a statement it said the Aquarius took on the migrants in worldwide waters off Libya and rescue operations were coordinated by Italy.
European Union law requires asylum seekers to register in the first safe country they reach, but frontline countries such as Italy and Malta say the burden needs to be shared out across the bloc.
"In the Mediterranean.there's Malta that does now welcome anyone, there is France that rejects [refugees] at its borders, there's Spain that defends its borders with the arms".
"This Europe is not showing solidarity", Prime Minister Giuseppe Conte said, adding that "Italy has to deal with the problem" of illegal human trafficking and migration flows "all by itself".
Salvini, in a joint statement with Italian coastguard minister Danilo Toninelli, insisted that Malta "cannot continue to look the other way when it comes to respecting precise global conventions on the protection of human life". "The priority of both the Italian and Maltese authorities should be ensuring these people receive the care they need", Commission spokesman Margaritis Schinas told a news conference.
Operation Themis, which replaced Operation Triton was put in effect earlier this year, meaning that Italy was no longer obliged to take all migrants rescued from the Mediterranean Sea.
"The boat is now heading north towards a secure port", SOS Mediterranee tweeted on Sunday without specifying its destination, though virtually every such migrant boat over the past five years has ended up in Italy. "We need to know who is arriving", a local man, Salvo Cavallaro said, "these 600 people, we don't know who they are".
The League promised voters during Italy's general election that it would take a tough stance on immigration, the BBC reported.
"If anyone thinks I won't move a muscle while we have another summer of landings, landings and more landings, well that's not what I'm going to do", Salvini told reporters.
Refugees and migrants are transferred to the SOS Mediterranee Aquarius rescue ship a day after being rescued by members of the Spanish NGO Proactiva Open Arms on Monday, May 7, 2018.
The agency was sent questions to assess whether any of the countries were violating their obligations to Frontex or any other worldwide agreements, and at which port should the migrants disembark.
We have always welcomed rescue boats and vessels who saved lives at sea.
Malta said the German charity SOS Mediterranee had picked up the migrants in Libyan waters, which meant they fell under Italy's jurisdiction.