The Italian Coast Guard said Tuesday it rescued more than 2,000 migrants from the dangerous seas off Libya over the last two days.
About 25 separate operations were needed to rescue the men, women and children from overcrowded boats.
Italian authorities say there were no casualties and that all the migrants were taken to Sicily.
Austria says it is planning to bring back tighter controls of its border with Italy, fearing a new influx of migrants.
Along with beefing up several existing border crossings, workers have started building a new border control checkpoint in the Brenner Pass which links Austria and Italy through the Alps.
The European Union says it is "very concerned."
"If these plans should materialize then we will have to look at them very seriously," spokeswoman Natasha Bertaud said. "The Brenner pass is essential for freedom of movement within the European Union."
Meanwhile, hundreds of migrants have already volunteered to evacuate a camp along the Greek-Macedonian border which has been the scene of violence, squalor and muddy misery.
Buses have been transporting the migrants out of the Idomeni camp to reception centers elsewhere in Greece and hundreds of others will likely follow.
Macedonian riot police fired rubber bullets and tear gas at migrants who tried to cross over from Greece Sunday.
Someone had scattered notices throughout the camp spreading a rumor that the border was open.
Greek authorities accuse the Macedonians of overreacting and is investigating where the false flyers came from.
Hundreds of thousands of men, women, and children trying to escape war, poverty and terrorism in Syria and Iraq have poured into the European Union with the EU struggling to cope.
A deal signed with Turkey would send new migrants arriving in Greece to Turkey in exchange for aid and other benefits for Turks.
Human rights groups criticize the deal, saying the EU is using human beings as political bargaining chips.
One discouraged Iraqi man in Greece told Reuters Tuesday he believes European authorities do not see the migrants as humans.
"Why is Europe not paying them any attention? Why won't they lend their humanitarian eye on them? Is it because we're Arabs? If This happened to Europeans and they came to us Arabs, wouldn't we welcome them?"