Family members of people believed to be held in jails run by Shia Houthi fighters and a secret prison network operated by the United Arab Emirates and its local allies have staged two separate demonstrations in the Yemeni capital Sanaa, demanding the release of their loved ones.

Both groups of protesters on Wednesday called for the intervention of the International Committee of the Red Cross (ICRC), whose head is currently leading a delegation to Yemen to secure family access to the prisoners.

An AP news agency investigation revealed in June that hundreds of men captured in the hunt for al-Qaeda in the Arabian Peninsula (AQAP) fighters had disappeared into clandestine lockups in southern Yemen.

Some Houthi-allied organisations have documented dozens of cases of Yemenis being held by UAE soldiers as prisoners of war. And some of the people originally held in the UAE-run prisons are said to have been moved out of Yemen.

Abuse in the prisons is routine and torture extreme - including the "grill", in which the victim is tied to a spit, like a roast, and spun in a circle of fire, the AP investigation found.

After the report was published, senior US defence officials acknowledged that American forces had been involved in interrogations of detainees in Yemen but denied any participation in or knowledge of human-rights abuses.

Interrogating detainees who have been abused could violate international law, which prohibits complicity in torture.

The government of President Abd-Rabbu Mansour Hadi on Tuesday allowed the ICRC delegation, led by Peter Maurer, to visit Houthi detainees in the south-western Taiz province.

"A promising step: today we were allowed to visit detainees in Taiz for the first time," Maurer said on Twitter.

"Now we need all parties to agree to regular visits."

The visit was the first since Yemen descended into civil war in 2014 when the Houthi fighters overran much of the country, including Sanaa.

Yemeni army's Colonel Abdo Hamouda al-Saghir said the delegation visited detained Houthi fighters and allied forces of the former Yemeni president, Ali Abdullah Saleh.

"The visit aimed to inspect conditions of the Houthi prisoners and their allies in the city," Saghir told Turkey's Anadolu Agency.

On Sunday, the ICRC delegation visited the southern city of Aden, the current seat of Hadi's government, for talks with Ahmad bin Dagher, the prime minister, on the humanitarian situation in the country.

According to the families of imprisoned soldiers, Hadi's government has recently sent an offer of a prisoner swap to the Houthi leadership through ICRC mediation.

More than 8,000 people have been killed and a further 44,500 wounded in Yemen since Saudi Arabia and its allies joined the conflict in March 2015.

According to UN officials, up to 11 percent of the Yemeni population has been displaced as a direct result of the conflict.