About a dozen ships from several countries, along with at least one private ship, were involved in rescue operations at four locales, said an Italian coast guard officer. They moved into action after the first distress calls came in early Saturday, U.N. Refugee Agency spokesman William Spindler said.
As of 11 p.m. (5 p.m. ET), an estimated 3,480 people had been rescued, according to the Italian Coast Guard officer, though that didn't mean many more people weren't still stuck and in danger.
"Weather and sea conditions are relatively good, and so far there have been no reports of accidents or of people dead or missing at sea," Spindler said.
Vessels from Italy, Great Britain, Germany and Ireland were involved in the rescues, officials said.
Ian Ruggier, a member of the humanitarian group Migrant Offshore Aid Station
, was on one of the rescue boats. He reported about 2,400 people being rescued off five boats -- four with about 560 migrants each, plus one smaller boat -- roughly 28 nautical miles (32 miles) off the coast of Libya.
Some rescue ships turned up with rescued migrants already on board, according to Ruggier. That's what happened with one German naval vessel that picked up 301 migrants from an unreported vessel as the German ship was on the way to the larger rescue scene, a spokesman for Bundeswehr Joint Forces Operations Command said.
The German ships went to the main site and found seven packed boats -- far more than they expected -- according to the spokesman for the command, which is part of Germany's military.
The Italian Interior Ministry reported that several of its own ships were involved, including from its coast guard and navy. The Italian rescue vessels are expected to arrive during the night at the island of Lampedusa.
The British Navy dispatched one of its own ships, the HMS Bulwark, to the area, according to the UK Ministry of Defence.
The HMS Bulwark had two helicopters onboard moved toward the migrants at a top speed of 17 knots (20 mph), according to the ministry. Defence Secretary Michael Fallon had been on the Royal Navy vessel at some point recently, though it was unclear if he was still there Saturday.
One Irish naval vessel was involved in the efforts, Spinder and Ruggier said.
Europe dealing with immigration crisis
The prospect of migrants being in jeopardy in the Mediterranean is serious but hardly surprising. People from impoverished and wartorn countries such as Syria, Somalia, Sudan and Eritrea have been taking to the sea to reach Europe in especially large numbers of late, often putting their fates in the hands of smugglers.
Many times they haven't made it. Hundreds of migrants died in April when their crammed 66-foot (20-meter) boat capsized
roughly 70 miles (113 kilometers) north of Libya. That got a lot of news coverage, but it didn't stop the carnage -- including dozens feared drowned after falling into the Mediterranean Sea last month
as a rescue vessel approached, according to the aid organization Save the Children.
The United Nations estimates that, as of the end of May, almost 90,000 refugees and migrants had crossed the Mediterranean into Europe so far this year. Just over half of them landed in Italy with roughly 42,000 in Greece and the rest recorded in places like Spain and Malta. Spindler, the U.N. spokesman, added that about 1,850 had died or went missing at sea.
Italian authorities noted that it's too early to tell if Saturday's efforts will break any records for the number of rescued migrants.
"We recently had around 5,000 rescued migrants in a day," said the Italian Coast Guard officer. "Today ... figures might be much higher."