The crews were trained in Italy "to monitor Libyan territorial waters...and contribute, together with Italy and Europe, to security in the Mediterranean", Minniti said in remarks translated into Arabic.
A Libyan naval officer told AFP the vessels had been due for delivery in 2014, but this date was pushed back because of violence and instability in the North African country.
Libya has long been a stepping stone for migrants seeking a better life in Europe. People smugglers have stepped up their lucrative business in the chaos which has engulfed the country since its 2011 revolution.
Minniti said on Monday another six patrol boats would be handed over to Libya soon after the training of the crews.
Libya's authorities have complained about lacking the means to deal with the floods of migrants who try crossing the Mediterranean in makeshift boats.
Italy registered nearly 42,500 migrant arrivals by sea by mid-April, 97 percent of them from Libya, Minniti said in a joint letter written with his German counterpart to the European Commission.
In the letter dated May 11th, which AFP obtained a copy of on Sunday, Minniti and Thomas de Maiziere said they "are convinced that we all must do more" to "prevent that hundreds of thousands of people once again risk their lives in Libya and on the Mediterranean Sea in the hands of smugglers."
Last year, a record 181,000 migrants reached Italy, 90 percent of them from Libya.
During his brief visit on Monday to Tripoli, Minniti also held talks with Government of National Unity head Fayez al-Sarraj on fighting illegal immigration.
READ MORE: The changing face of the Mediterranean migrant crisis
Photo: Andreas Solaro/AFP