About 6,500 migrants have been rescued off Libya, the Italian coastguard says, in one of the biggest operations of its kind to date.

Some 40 co-ordinated rescue missions took place about 20km (12 miles) off the Libyan town of Sabratha, it added.

Video footage shows migrants, said to be from Eritrea and Somalia, cheering and some swimming to rescue vessels, while others carried babies aboard.

On Sunday more than 1,100 migrants were rescued in the same area.

The instability in Libya has made the country a hub for people-trafficking.

Monday's operations involved vessels from Italy as well as the EU's border agency Frontex and the NGOs Proactiva Open Arms and Medecins Sans Frontieres (MSF).

The migrants had set off in overcrowded and unseaworthy vessels with enough fuel to reach waiting rescuers, AP reported.

Last year more than one million migrants – many fleeing the civil war in Syria – arrived in Europe, sparking a crisis as countries struggled to cope with the influx, and creating division in the EU over how best to deal with resettling people.