Mediterranea's Italian-flagged Alex was met by a strong police presence on the quayside but people were not allowed to disembark after spending two days with the rescued migrants and asylum seekers on the sailboat.
"I do not authorize any landing for those who couldn't care less about Italian laws and help the people smugglers," populist Deputy Prime Minister Salvini tweeted as night fell, Presstv Reported.
Salvini last month issued a decree that would bring fines of up to 50,000 euros ($57,000) for the captain, owner and operator of a vessel "entering Italian territorial waters without authorization."
After the Alex reached port, he said that he would raise the maximum fine to one million euros.
Mediterranea tweeted back a request to disembark those rescued, saying it had sailed to "the only possible safe port for landing", citing "intolerable hygiene conditions aboard".
"Shipwrecks and crew are exhausted... people rescued need to be cared for... this is a surreal situation and it is an unnecessary cruelty to prolong the wait."
Authorities on Lampedusa last week seized another rescue ship belonging to German aid group Sea-Watch after it forced its way into port with dozens of rescued migrants on board and arrested its captain, Carola Rackete.
An Italian judge this week ordered her freed as she had been acting to save lives, a decision which sparked Salvini's ire but may have encouraged the Alex crew.
Two other investigations, on charges of helping people smugglers and resisting the authorities are still underway after Rackete forced her way past Italian customs vessels.
A third rescue ship, German charity Sea-Eye's vessel Alan Kurdi, carrying 65 shipwrecked migrants rescued off Libya had also arrived in international waters off Lampedusa.
The group said late Saturday that it was heading for Malta.