The migrants will be transferred from the Sea-Watch 3 and Albrecht Penck ships to Maltese coastguard vessels "as soon as possible", Muscat said.
However the 49 migrants, including women and children, were allowed to disembark in Malta on Wednesday after a deal was struck.
The 49 migrants, including a baby and several children, were rescued while attempting the unsafe Mediterranean crossing from North Africa to Europe.
Malta's Prime Minister Joseph Muscat addresses a press conference at his office in Valletta, Malta January 9, 2019.
A ship operated by German rescue group Sea-Watch picked up 32 people on December 22.
EU Migration Commissioner Dimitris Avramopoulos said Wednesday that "the past weeks have not been Europe's finest hour".
The migrants were brought to shore by the Armed Forces of Malta (AFM) after they were transferred at sea from the two ships that were carrying them.
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Sea-Watch said that the migrants finally have a "safe haven" after three weeks at sea. "This represents a confession of state failure, policy must not be made at the expense of people in distress".
"An ad hoc agreement has been reached", said Muscat.
He again defended his decision to refuse to let the ships dock, although Malta had allowed them to enter its waters for supplies and to shelter from bad weather.
While Italian Prime Minister Giuseppe Conte has been involved in efforts to broker an agreement and Deputy Prime Minister Luigi Di Maio had called for Italy to take in all women and children on board, Interior Minister Matteo Salvini - who is also a deputy prime minister - repeated his assertion that no migrants would be allowed to land, accusing the European Union of "giving in to the blackmail of people smugglers and NGOs" and saying he had not been consulted about the deal.
Italy's populist government split over the fate of those aboard Sea-Watch 3 and another private vessel, Sea-Eye, with Premier Giuseppe Conte saying that Italy was willing to take children and their parents, even as Mr Salvini remained defiant.
The European Union's border agency Frontex says about 57,000 migrant crossings were detected previous year in Spain, double the figure for 2017.