Italy demanded an apology after the French president accused the new Italian government of irresponsible behavior for refusing entry to a rescue ship with 629 migrants aboard.
Italian Interior Minister Matteo Salvini, of the anti-immigrant League, has spearheaded a hardline stand on curbing arrivals from across the Mediterranean as a priority for the new populist coalition with the anti-establishment Five Star Movement.
The Spanish authorities then said they were ready to let the Aquarius dock in its eastern port of Valencia.
Rome called his comments "unacceptable" and summoned France's ambassador on Wednesday.
But the talks were delayed as both countries traded barbs over the fate of more than 600 migrants rescued off the Libyan coast on the weekend.
"We're doing a lot but it's true: Europe must do more and must do better to help Italy", she said.
This comes as the Italian government has urged its European counterparts to take in more asylum seekers.
Salvini also accused France of having turned back 10,249 migrants at Italy's northern border since January, "including women, children and disabled people".
SOS Mediterranee said men who were still on the deck of the Aquarius and exposed to the elements were dizzy and vomiting, and taken inside the ship to be treated for seasickness.
"Such statements are undermining relations between Italy and France", Italy's foreign ministry said in a statement Wednesday.
United Nations refugee chief Filippo Grandi urged the European Union on Wednesday to sort out its "shameful" refugee policy after both Italy and Malta turned away a ship carrying hundreds of migrants.
A government source said Conte still did not see the right "conditions" for a Friday meeting with Macron.
"We believe an axis of the willing is needed to fight illegal migration".
Italy's new government is demanding other countries take rescued migrants.
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.
That has put pressure on Italy and Greece, the entry points for the hundreds of thousands of people fleeing war and poverty.
He called for stronger external controls, cooperation with Africa, sending home migrants who were not entitled to remain, and countering traffickers.
A boat loaded with 55 people who were thought to be Syrian refugees landed Wednesday on the northwest coast of Cyprus, a Mediterranean island split into ethnically Greek and Turkish sides.