In a recorded interview set to air on Sunday, Muscat said that despite the fact that the boat is now within the Maltese rescue zone, Malta does not have any obligations towards it.
Interior Minister Matteo Salvini initially said in a post on Facebook that the two NGO ships should "go to Holland", as it was said to be flying under a Dutch flag, and should not dock in Italy.
"For the safety of the crew and passengers we have asked Malta to open its ports", the leader of the far-right League tweeted, claiming the vessel was in Maltese waters. But the Aquarius defiantly vowed to continue its work and an AFP photographer on board said Saturday that it was now responding to distress call in Tunisian waters.
While Merkel won global accolades for her generosity towards migrants, she is now weaker than ever at home over her refugee policy.
The figure was a "conservative estimate", United Nations spokesman William Spindler said in Geneva on Friday.
Hungary meanwhile passed a law today criminalising aid groups that help migrants.
Muscat said that the boat did not follow instructions from the Italian and Libyan authorities when it began sailing towards Italy.
Mr Macron said he would back financial sanctions for the bloc's 28 nations if they fail to take in a flurry of refugees that have proven asylum status in a move that has fanned the flames of the Brussels immigration crisis.
The latest Italian message represents a change in policy from the coastguard which has often played an important role coordinating migrant rescue missions in the Mediterranean outside of its search and rescue area.
The Lifeline is carrying 226 migrants rescued off the coast of Libya, Mission Lifeline said.
Italy's new populist government has threatened to seize several other ships carrying migrants, sparking a row with the EU.
Salvini's tough talk came on the eve of an informal mini-summit of 16 leaders in Brussels to address the thorny issue of how the European Union can tackle the renewed influx of migrants and refugees seeking a new life in Europe.
More than 2,300 children have been taken from their parents since early May, a practice loudly decried by rights groups and USA politicians from both main parties.
Chancellor Angela Merkel's conservative allies on Wednesday took aim at her backing for a new eurozone budget, German media reported, opening up another front in their attack against her.
But a government spokesperson told this newspaper that the captain of the vessel refused the medical evacuation, saying that no assistance was needed.
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 neighbors 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.
News of rescue ships being turned away from European ports comes as the EU bloc grapples to find a solution to the refugee crisis.