At least 20 migrants, some of them young children, have drowned after falling into the sea off the Libyan coast, Italy's coastguard says.

The overcrowded boat was carrying about 500 migrants and a rescue operation is under way, reports say.

"There's a critical situation... about 200 people fell into the water," a coastguard spokesman said.

The central Mediterranean route for illegal migration to Europe is currently the busiest. 

More than 50,000 migrants have reached Italy this year.

The route is also the most deadly, accounting for the vast majority of the 1,364 people who the UN estimates have drowned in the Mediterranean this year.

One report suggested a private humanitarian group, Moas, had begun lifting people from the crowded wooden boat about 30 nautical miles off Libya, when many fell into the water. 

It is thought they may have been knocked off balance by a wave.

Chris Catrambone of Moas tweeted pictures from the scene and said bodies were still in the water - including those of toddlers.

The Italian coastguard has sent other boats to the scene. A helicopter and military aircraft were dropping lifeboats, said AFP.

Good weather conditions off Libya have prompted an increase in the number of migrants leaving for Italy.

Reports say there are currently operations under way to rescue people from some 15 vessels off Libya, reportedly carrying 1,700 people.

Libya is a gateway to Europe for migrants from across sub-Saharan Africa and also from the Arabian peninsula, Egypt, Syria and Bangladesh. Many are fleeing war, poverty or persecution.