He also said that between January and May, France had sent back to Italy 10,249 migrants who had crossed their common border.
"If an official apology doesn't arrive, Prime Minister Conte would be right not to go to France", Salvini told reporters.
The dispute began when French President Emmanuel Macron on Tuesday denounced the "cynicism and irresponsibility of the Italian government" for its handling of the Aquarius migrant rescue ship earlier this week.
The migrants aboard the Aquarius, run by French NGO SOS Mediterranee, were stuck on the overloaded ship as Italy and Malta bickered over who should take them. Italian maritime vessels, however, are still docking in its ports.
The move comes hours after Italy summoned the French ambassador to the foreign ministry in Rome.
"The statements concerning Aquarius from France are surprising", the Italian Council stressed, adding that Rome won't tolerate receiving "hypocritical lessons from countries that preferred to divert the head "on the migrant crisis".
Yet Slovakia's premier insisted that "we refuse to let migrants enter our country", a stance that could bring him into conflict with Italy's new leaders, who have called for the automatic, compulsory resettlement of migrants across all European Union countries.
France sought to take a more conciliatory tone on Wednesday.
UK's Theresa May says Russian Federation must change before it returns to G8
Trump was due to arrive in Singapore on Sunday ahead of a historic summit with North Korean leader Kim Jong Un . The bloc includes China, Russia along with four ex-Soviet Central Asian nations, as well as India and Pakistan.
Ms Merkel spoke after Interior Minister Horst Seehofer, a top CSU leader, called for Germany to ally itself with Austria, governed by a right-wing coalition, and Italy on migration and security policies.
"The law is when a boat is in trouble it's the country and the port that's closest that provides the rescue", Le Drian said.
Salvini has repeatedly vowed to stem the flow of migrants to Italy, which has seen more than 700,000 arrive on its shores since 2013.
The case has reopened one of the main unresolved faultlines in European politics: how to share responsibility for migrants trying to enter the bloc from conflict zones and poor countries, mainly across Africa and the Middle East.
Mr Salvini said he plans to visit his conservative German counterpart in Berlin soon to hammer out new proposals on the boat row and the broader issue of migrant quotas.
Salvini has accused European aid groups of essentially operating taxi services for Libya-based human traffickers, and has said Italy will now refuse them entry. "The coastguard and navy can continue to save lives, but other countries need to keep giving us a hand", he said.
On Wednesday morning, an Italian coast guard vessel with 937 migrants and two bodies aboard docked in Catania, Sicily, while the Aquarius headed into increasingly rough seas on its way to Valencia, where it is due to arrive on Saturday.