Italian coast guard ships, along with military vessels from Ireland and Britain, have rescued at least 2,900 migrants from 21 smugglers boats in the Mediterranean, north of Libya.
An Irish military statement said the Irish vessel Le Eithne was involved in six of the operations on Sunday, rescuing migrants from inflatable rubber dinghies.
In a statement, the Italian coast guard also confirmed the number.
About 100 of the migrants were being brought to the tiny island of Lampedusa, off Sicily. Authorities were determining which larger, southern Italian ports would receive the others on Monday.
So far this year, about 60,000 migrants saved by ships in a multi-nation search and rescue mission have been brought to Italian ports.
Many seek asylum from wars or persecution in Africa or the Middle East, and hope to reach families in northern Europe.
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Struggling under the influx, Italy wants northern European countries to take in fixed numbers of migrants.
EU discussions about Italy's appeal have so far only yielded plans for such help on a voluntary basis.
The EU wants to oblige member countries to share 40,000 Syrians and Eritreans requiring international protection who are expected to arrive in Italy and Greece over the next two years.
But many of the 28 nations are refusing to have migrant numbers dictated to them from Brussels.
About a dozen nations oppose the EU plan. A further 12 that would support it want the method for sharing out the refugees reassessed.
The 'distribution key' foreseen by the EU takes into account the population, economic strength, unemployment rates and current efforts already undertaken to help refugees.
Lithuanian President Dalia Grybauskaite said that her country would participate "but on a voluntary basis."
While EU leaders have made pledges to help frontline migration countries in the past, their promises have often disappeared once the media spotlight dims.