The Naval Service patrol ship LÉ Niamh rescued 125 people off a rubber craft 60 kilometres north east of Tripoli on Sunday.
A north-westerly force 5 wind made sea conditions difficult throughout the rescue.
The LÉ Niamh was alerted to the rubber craft by a merchant ship, the St Jeneborg which was sailing in the area. The Irish naval vessel got to the scene at 2 pm with all people embarked by 4 pm.
The 125 rescued migrants on board are receiving water, food and medical assistance.
The LÉ Niamh had rescued 3723 people before today’s operation.
Meanwhile, thirteen migrants died after a boat collided with a ferry off the Turkish coast on Sunday, the coast guard said.
Turkey’s coast guard agency said in a statement that it intervened after being alerted that a commercial vessel hit a migrant boat off the western port city of Canakkale and that bodies were in the water.
Six of those killed were children and 20 others were rescued, the source said. Seven of those rescued were receiving treatment.
The search continues to find 13 missing people.
H ungary erected a steel gate and fence posts at a border crossing with Croatia on Sunday, moving to seal a route used by its southern neighbour to offload thousands of migrants, a Reuters cameraman said.
Croatia has sent dozens of buses packed with migrants through the Baranjsko Petrovo Selo - Beremend crossing since they began streaming over its eastern border with Serbia five days ago.
More still have crossed by train, boarded by hundreds in chaotic scenes repeated on Sunday when rain-soaked migrants climbed through carriage windows at the Croatian border station of Tovarnik.
Hungary has barred their entry into the European Union via its border with Serbia with a metal fence and a raft of strict asylum rules, forcing them west into Croatia.
Fast losing control over an influx of some 25,000 migrants, Croatia - the EU's newest member - has taken to sending them north by bus and train across its own border with Hungary, which has waved them on to Austria.
The move has triggered angry exchanges between Zagreb and Budapest indicative of the disarray in Europe over the largest migration of people westwards since World War Two.
Hungary, which says it is defending Europe’s “Christian identity” from hundreds of thousands of mainly Muslim migrants reaching its shores, says it is completing another fence on a 41 kilometre stretch of its frontier with Croatia to keep them out.
A Reuters cameraman on the Croatian side of the border saw construction crews and soldiers erecting a gate and driving fence posts some three metres high into the ground, suggesting they were close to sealing the Beremend crossing.
More migrant buses were on their way from the nearby Croatian town of Beli Manastir.
Further south, on Croatia’s border with Serbia, a packed train left the town of Tovarnik amid desperate scenes of migrants running and fighting to board, and small children plucked from the crowd by startled and overwhelmed police.
After several hot days, the temperature dropped overnight and rain arrived on Sunday. “I’m desperate,” said 32-year-old Amina, travelling with two children from Baquba in Iraq.
“It was cold overnight and now it’s raining and the children will get sick,“ she said through a Red Cross interpreter. “The police say they will board women and children first, but I didn‘t manage. I lost our bag the day before yesterday and now we have no belongings at all.”
Police in Germany said on Sunday there had been an arson attack on a planned accommodation centre for migrants in the southwestern state of Baden-Wuerttemberg, the latest sign of tension as migrants flow to the country.
Police in the city of Heilbronn said no-one had been in the sports hall in nearby Wertheim at the time of the attack and it was not possible to enter the building because of fire damage.
The attack came as a senior member of parliament in Chancellor Angela Merkel's conservative sister party, the Christian Social Union (CSU), spoke out in favour of tighter rules on granting asylum.
"Those who are not in danger should leave Germany as quickly as possible," Gerda Hasselfeldt told the Welt newspaper.
“We have to set clear priorities. We need our energy and resources for those who are fleeing war and persecution.”
The comments came as Hungary and Croatia traded threats as thousands of migrants poured over their borders, deepening the disarray in Europe over how to handle the crisis.
A proposal being argued over ahead of a meeting of European Union interior ministers on Tuesday would, if agreed, relocate 120,000 asylum seekers over the next two years around the whole bloc.
The number of migrants entering Germany, which recently reimposed border controls, was lower on Saturday, with 1,710 people registered, than on Friday, when the number was 1,985, police said.