Malta last week allowed the boats to shelter near its coasts from the bad weather but would not let them disembark the migrants.
"The head of the Federation of Evangelical Churches in Italy (FCEI), Luca Maria Negro, said in a press release, shortly after Malta's announcement: "[FCEI] has told the Interior Minister we are available to welcome some of the refugees from Sea-Watch who are arriving in our country.
A mother and a child disembark from a patrol boat in Malta.
Joseph Muscat, prime minister of Malta, announced the details that end the deadlock that began when 32 people were rescued by the Dutch-flagged humanitarian rescue ship "Sea-Watch 3" on 22 December.
Interior Ministry spokesman Steve Alter stressed in Berlin Wednesday that the move for European Union countries to share out numerous 249 migrants already rescued by Maltese military ships - plus 49 who have been stranded aboard private rescue vessels - is "an ad hoc decision ... for the current situation".
In a tweet, Sea Watch International said: "The EU made a decision to release their 49 hostages. Every hour that passed without a solution was not an hour I was proud of", he said.
"It is a testament to state failure; politics should never be played at the cost of people in need."
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Alter said eight countries have now indicated their willingness to take in the migrants but talks are ongoing with more.
Malta has reached a deal with other European Union member states to allow 49 migrants aboard two rescue ships off the coast of the island nation to disembark.
Many people have been heading to Europe from Africa and the Middle East across the Mediterranean in a flight from poverty or armed conflict.
The exact number of migrants that Italy has agreed to host has not been announced, but Conte had previously indicated that Rome was willing to welcome around 15.
Police in Spain said Wednesday they broke up a gang that allegedly smuggled people and drugs on boats from Morocco and charged migrants up to 2,000 euros ($2,300) a trip.
Mr Avramopoulos said the fact that some of the migrants had to wait at sea for three weeks "is not what the European Union stands for".
The European Union's border agency Frontex says about 57,000 migrant crossings were detected previous year in Spain, double the figure for 2017.