The ship, escorted by two Italian vessels, is not expected to dock on the Italian island as it continues its journey to Valencia, Spain, where authorities have offered safe harbour for the 629 people the boat rescued from the Mediterranean last weekend.
Will the new Italian prime minister still be coming for lunch Friday?
Pope Francis called on Thursday for a "change in mindset" on migration policies, saying global cooperation was vital, as Italy and France engaged in a diplomatic spat over the issue. "We need to maintain dialogue", a source close to Macron said as the president visited the western town of Rochefort.
Italy's refusal to accept the ship marked the first major anti-migrant move since far-right interior minister Matteo Salvini took office in June.
SOS Mediterranee, the aid group that operates the Aquarius, said Thursday the Italian coast guard boat leading the convoy made a decision to skirt Sardinia's east coast after high waves caused exhausted migrants aboard to be seasick.
The asylum seekers remained stranded on the Aquarius vessel, run by French NGO SOS Mediterranee, while Italy and Malta bickered over who should accept them.
More than 1.8 million people have entered Europe since 2014, with more than 600,000 arriving in Italy.
"Such statements are undermining relations between Italy and France", Italy's foreign ministry said in a statement Wednesday.
Salvini has repeatedly accused fellow European Union members of abandoning Italy as it struggles to cope with an influx of migrants making the perilous journey across the Mediterranean. He declared his support for Kurz's proposal for a three-way "axis of the willing" with Italy to fight illegal migration.
France is "perfectly aware" of the pressure on Italy as it copes with an influx of migrants from Africa, a foreign ministry spokeswoman said.
But member states remain deeply divided over burden-sharing plans aimed at warding off any repeat of the 2015-16 migration crisis, with "frontline" states like Italy, Greece and Spain complaining they are shouldering an unfair share of arrivals, wealthier destination countries such as Germany and the Netherlands arguing they have done enough, and hardline central European governments including Hungary and Poland flatly rejecting all compulsory refugee distribution schemes.
"With my German and Austrian colleagues. we will propose a new (immigration) initiative", Salvini said, adding that it would apply both to the EU's external borders and to how the bloc's countries manage migrants internally.
Salvini has accused charities that rescue migrants of working with human traffickers but said Italy would not stop rescuing migrant boats itself.
More than 900 people have arrived at the Italian port of Catania in Sicily after being rescued at sea by the Italian Coast Guard.