At least two migrants died on Sunday in a fire at a Greek island refugee camp, with the blaze triggering rioting by angry residents.

Athens News Agency, quoting police sources, reported that a woman and a child had died in the blaze at the overcrowded Moira camp on the island of Lesbos.

The body of the woman was taken to the island's general hospital while the body of the child was handed over to authorities by migrants.

The fire inside the camp was extinguished by an airplane. But police later fired tear gas to control a crowd angered by the time it had taken, according to an AFP correspondent.

The death toll, however was unclear with an Afghan migrant eyewitness saying three people died in the blaze that spread to six or seven containers used to house residents.

"We found two children completely charred and a woman dead. We gave the children covered in blankets to the fire brigade," Fedouz, 15, told AFP.

The AFP correspondent saw two bodies, one surrounded by weeping migrants.

In a statement, police said the riots occurred after two separate fires broke out, firstly outside and then inside Moria camp with a time gap of twenty minutes.

Additional officers were sent from Athens in C-130 army airplanes in a bid to contain the situation.

The Deputy Minister of Citizen Protection Lefteris Economou, along with the Chief of Police and the Secretary General for Migration Policy, were also heading to Lesbos.

Moria camp hosts around 13,000 people but has facilities for just 3,000.

It has become like a small town with UN refugee agency tents for around 8,000 people sprawling into the olive fields of nearby Moria village. Others are housed in containers.

-New asylum law-

Greece is hosting some 70,000 mostly Syrian refugees and migrants who have fled their countries since 2015, and crossed over from neighbouring Turkey.

Under an agreement reached with the European Union in 2016, Turkey has made greater efforts to limit departures towards the five Greek islands closest to its shores.

But the number of arrivals has been steadily climbing in recent months causing a dangerous burden in the camps of the islands that are in the forefront of the migrant influx.

The Greek government said on Sunday it planned to discuss a new asylum draft law to deal with the fresh migrant crisis.

"In the cabinet meeting on Monday, we are going to discuss a draft law proposed by the Citizen's Protection Ministry which will update, in accordance with European standards, the asylum procedure", Minister of State, George Gerapetritis said in an interview with Skai Tv on Sunday.

He stressed that migrants should be sent to camps with humane conditions, admitting that existing ones were not able to deal with the increase in migrants.

On Friday, Citizen's Protection Minister, Michalis Chrysochoidis, asked for the cooperation of regional governors, during an emergency meeting, in order to share the migrant burden of the overcrowded islands.

He asked regional authorities of mainland Greece to expand existing camps or to revive some closed ones.