The Spanish government said it is expecting ships carrying 630 migrants to arrive in the port of Valencia on Sunday morning instead of Saturday after bad weather forced the convoy to take a detour.
Mr Macron accused Rome earlier this week of acting with "cynicism and irresponsibility" after it turned away a migrant rescue boat with 629 people, including 11 children and seven pregnant women, on board.
Italy's new far-right interior minister Matteo Salvini has a hardline stance on immigration. Muscat highlighted however that Malta was willing to help avoid humanitarian crises.
Spain stepped in and said the migrants could land at the port of Valencia.
French President Emmanuel Macron denounced the block on the Aquarius, insisting that Italy should have taken the migrants in.
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. Rome says the rescue vessel's passengers never were in danger and argues that other European countries must share the work of welcoming would-be asylum-seekers.
Salvini, who is also deputy premier and the leader of the anti-immigrant League party, called on France to apologise and said he was not prepared to take criticism from a country which regularly stopped migrants on their shared border.
Grandi said that, even if the European Union succeeded in helping transit countries to manage the migrant flows before they arrive in Europe, "some people will continue to want to seek asylum in Europe".
Despite criticism from the pope and the United Nations refugee agency, which called the treatment of the migrants on the Aquarius "shameful", Salvini has not changed his position.
"We hope this meeting will be able to take place very quickly", he said in a ministry statement.
A government source said Conte still did not see the right "conditions" for a Friday meeting with Macron.
The French president's office said France didn't want to "start a precedent" that would allow some European countries to breach worldwide laws and rely on other EU member states to take in migrants.
Macron suggested Rome was trying to make a high-profile break with previous governments in refusing to accept the ship instead of tackling the underlying problems of development and security in migrants' home countries and smuggling rings.
Under the EU's asylum laws - now the subject of a major political dispute and under revision - migrants must apply for asylum in the country where they first enter Europe.
Conte said he and Macron "agreed on the need to cooperate closely" on migration issues.
Italian maritime vessels, however, are still docking in its ports: on Wednesday, an Italian coast guard vessel docked in Catania, Sicily with 932 migrants aboard. In practice, the policy has placed a heavy burden on Italy and Greece, where hundreds of thousands of asylum-seekers have arrived in recent years.