Altogether, groups rescued migrants from six boats and a barge, the Italian coast guard said.
One of the groups, the humanitarian organization Doctors Without Borders, or Medecins Sans Frontieres, said via Twitter that 797 people -- including 205 women and 22 children -- were transferred to its ship, the Argos.
All of them were "extremely relieved to be on board" the Argos, MSF said.
The nongovernmental organization Migrant Offshore Aid Station, which was also involved in the rescue effort, said via Twitter that the situation was under control.
MSF highlighted the rescue of a woman named Rachel and her young son, who the group said had fled Eritrea and traveled across the Sahara before embarking on the sea crossing.
Despite the efforts of NGOs and European coast guard and naval vessels, many such migrants do not survive the perilous journey.
In October, 2016 became the deadliest year for migrants
crossing the Mediterranean bound for Europe, the UN refugee agency said. The number believed dead or missing at sea
is more than 4,200 to date.
Those seeking to make the journey from Libya are at greatest risk, the agency said.
Libya is a popular jumping-off point for migrants seeking to reach Europe from North Africa. Smuggling networks are well-established there, and the lack of an effective central government makes the job of traffickers easier.
But the crossing can be treacherous, with too many migrants -- some fleeing war or persecution, others seeking a better life -- crammed into what are often barely seaworthy boats.
The European Union border agency, Frontex, said Monday it had helped in the rescue of more than 87,000 people between January and October in its operations off Italy and Greece.