"Our only objective is the disembarkation in a port of safety of the people that we rescued yesterday in hard conditions", it said, adding that it "took good note" of the Italian Interior Ministry's statements.
Early on Tuesday morning, the coordinator for the non-profit aid group Doctors Without Borders, which has staff aboard the Aquarius, confirmed that the journey to Spain will go ahead.
The 629 rescued migrants on board the ship Aquarius, operated by SOS Mediterranee and Doctors without borders, come from Eritrea, Ghana, Nigeria and Sudan, and include 88 women - seven of which are pregnant - 123 unaccompanied minors and 11 children.
The head of the anti-immigrant party, the League, Salvini has positioned himself as the strongman in the unlikely coalition government recently formed with the ideologically fungible Five Star Movement.
"This plan would mean already exhausted rescued people would endure 4 more days travel at sea", it said on Twitter.
After Spain's new Prime Minister Pedro Sanchez allowed the ship to dock in Valencia, Salvini celebrated the decision.
Given that the aid ship had no emergency, Italy chose to appeal to other European countries "so they don't leave Italy alone yet again in managing the migratory flows, which is a phenomenon that is all of Europe's business", Di Maio said in a Facebook post.
The Aquarius received 129 people from one Italian coastguard ship (CP 312), 64 from a second Italian coastguard ship (CP 319), and finally 88 from a third Italian coastguard ship (CP 267).
Aquarius remains in worldwide waters off Malta and Italy, the countries with the closest ports of safety but which continue to refuse permission to dock.
The French government issued a pointed response to Italy's decision.
The Spanish government said it would accept the ship at the port of Valencia.
The charity added the boat is carrying several critical drowning and hypothermia patients who had to be resuscitated, as well as several with chemical burns caused by being exposed to a toxic mixture of sea water and fuel for a long time.
The dispute was among the first consequences of political upheaval in Italy, where anti-migrant leaders recently rose to power with a pledge to crack down on new arrivals from the Middle East and Africa.
Migrants on a rubber boat are rescued by the SOS Mediterranee organisation during a search and rescue operation with the MV Aquarius rescue ship (background) in the Mediterranean Sea, September 14, 2017.
"We call on all involved to contribute to a swift resolution so that the people on board the Aquarius vessel may be safely disembarked as soon as possible".
Sky News says "the refusal - a realisation of tough anti-immigration promises made by Italy's new government - left those on board in mortal danger and prompted a diplomatic spat over the future of migrants travelling across the Mediterranean".