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The heads of six United Nations agencies and three international NGOs issued a joint call on Thursday for the release of their staff detained by Yemen's Iran-backed Houthi rebels.

They said the detentions were unprecedented and insisted the targeting of aid and development workers in Yemen must stop.

"We, the principals of the affected UN entities and international non-governmental organisations, call for the immediate and unconditional release of all personnel held in Yemen by the Houthi de facto authorities," the joint statement said.

"We are extremely concerned about the Houthi de facto authorities' recent detention of 17 members of our organisations and many others associated with civil society organisations, national and international NGOs, and other organisations supporting humanitarian activities."

The statement was signed by the heads of the UN health, food, human rights, development, culture and children's agencies.

It was also signed by the heads of Oxfam International, CARE and Save the Children International.

UN human rights chief Volker Turk said Tuesday that 13 UN personnel had been detained, including six members of his own staff.

"These detentions are unprecedented - not only in Yemen but globally - and directly impede our ability to reach the most vulnerable people in Yemen, including the 18.2 million people who need humanitarian aid and protection," Thursday's joint statement said.

They urged the Houthis to confirm the exact whereabouts of those detained and the conditions in which they are being held, and demanded immediate access to them.

International Humanitarian Law requires all parties to armed conflict to respect and protect humanitarian personnel, including against harassment, mistreatment, and unlawful arrest or detention, they added.

The UN and aid groups said last week that the detention of staff appeared to be a coordinated move.

The Houthis said they had arrested "an American-Israeli spy network" operating under the cover of humanitarian organisations - claims Turk rejected as "outrageous".

The Houthis are engaged in a long-running civil war that has triggered one of the world's worst humanitarian crises. More than half of the population is dependent on aid in the Arabian Peninsula's poorest country.

The rebels seized control of the capital Sanaa in September 2014, prompting a Saudi-led military intervention on behalf of the government the following March.

They Houthis have kidnapped and tortured hundreds of civilians since the start of the conflict, according to Human Rights Watch.