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

After the fire was extinguished, police fired tear gas to control a crowd angered by the time it had taken for the fire brigade to arrive at the Moira camp on the island of Lesbos, according to an AFP correspondent.

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

Athens News Agency, quoting police sources, reported that a woman and a child had died in the fire.

An Afghan migrant eyewitness, however, told AFP a woman and two children had died, describing how the blaze 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, said.

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

Migrants said they were angry over the time it took for the fire brigade to arrive, claiming that a long delay had led to the fatalities.

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.

The 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.

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.