Yemen's Huthis expressed "deep regret" Wednesday over the deaths of dozens of migrants in a fire which Human Rights Watch said started when the rebels fired projectiles into a detention centre.

A senior official in the rebel movement, which is locked in a six-year campaign against the internationally recognised government, said that an investigation into the March 7 incident was under way.

"We express our deep regret over the accidental incident at the migrant detention centre in Sanaa," said Huthi official Hussein Al-Azi, according to the rebels' Al-Masirah television.

"The victims are 44 migrants and the wounded are 193, most of whom have gone to hospital, and there is an investigation into the reasons for the incident."

The United Nations called Tuesday for an independent investigation into the blaze, shortly after Human Rights Watch blamed it on "unidentified projectiles" fired by the Huthis.

"There must be an independent investigation into the cause of the fire," the UN envoy for Yemen, Martin Griffiths, told the Security Council.

The Iran-backed rebels control much of northern Yemen, including the capital Sanaa which was captured from the Saudi-backed government in 2014, sparking the devastating conflict.

HRW said detainees had been protesting against overcrowding when camp guards rounded up hundreds of them into a hangar and fired two projectiles into the building.

The rights group said hundreds of injured migrants were being treated in hospitals in Sanaa where a "heavy security presence" had posed problems for humanitarian agencies seeking access. 

It cited interviewees as saying they saw the Huthis rearrest migrants who were not severely injured. 

Despite warnings, migrants from the nearby Horn of Africa continue to transit through war-torn and impoverished Yemen, seeking a better life in wealthy neighbouring Gulf Arab states.