The stand-off over the Dutch-flagged ship run by German charity Mission Lifeline mirrored a similar situation with migrant rescue ship Aquarius, which was left stranded at sea for days before being let into Spanish ports.
Italian Interior Minister Matteo Salvini has repeatedly called on Italy’s neighbours to share the burden of migrants.
"For the safety of the crew and those rescued we humanly and politically ask Malta to finally open one of its ports, and then seize the ship and its crew," Mr Salvini said in Siena, Italy.
Malta, a small island nation, has not taken in large numbers of people rescued at sea, while Italy has seen 650,000 arrivals since 2014.
On Friday, Malta had not received a call for help from the ship, Lifeline, or from Italy's coastguard, Maltese government sources said.
Lifeline was sailing about half way between Tripoli and Malta early on Friday.
"Malta cannot back out," Transport Minister Danilo Toninelli, who oversees the coastguard, said.
The European Union's border control agency Frontex "will make an official request to Malta to open its ports", he said.
On Thursday, Toninelli said the Italian coastguard would pick up the 224 migrants, including 14 women and four small children, from Lifeline because it was too dangerous for the 32-metre vessel to travel to the Netherlands with so many on board.
He said the coastguard would escort Lifeline to an Italian port, where it would be impounded pending an investigation into its flag status after the Dutch government denied responsibility for the vessel.
While the number of sea arrivals to Italy has dropped dramatically this year - more than 77 percent from last year - the new government has thrust immigration to the top of the EU's agenda ahead of a summit of leaders next week.
Italy's government, sworn in earlier this month after promising to raise its voice on immigration in Brussels, has sparred with France, Malta and Germany ahead of the meeting.