The emergency rescue came on the same day Italy said it was evacuating staff from its embassy in Libya and suspending operations there, highlighting the worsening security situation in the violence-plagued country.
Some 2,164 migrants coming from Libya had to be saved from a dozen boats, Italian media reported, citing the country's emergency services.
By yesterday evening around 520 migrants were on board an Italian navy ship, the TGcom24 television station's website said.
The Italian transport ministry said some of its coastguards had been threatened by four armed men earlier in the day who approached them by speedboat from the Libyan coast.
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The Kalashnikov-wielding men forced the rescuers to return a boat that had been emptied of migrants, the ministry said in a statement.
Last year, more than 3,200 people died while attempting to reach Italy by boat from North Africa. The United Nations has described the sea crossing as the most dangerous route in the world.
But in a major tragedy last week, more than 300 migrants died in the Mediterranean Sea when their overcrowded rubber dinghies collapsed and sank in stormy weather.
The victims were among migrants mainly from sub-Saharan Africa who had embarked on the perilous journey from a beach near Tripoli.
The deaths underscored the limited means and scope of Triton, an EU-run mission which took over in November from the Italian navy's Mare Nostrum search and rescue operation.
Italy has seen a surge in migrants leaving in boats from Libya as the country has sunk deeper into chaos.
The Italian foreign ministry yesterday said it was pulling out staff from its embassy in the former colony.