Yemen's Houthi rebels are holding dozens of women without trial and often torturing the detainees and blackmailing their families, activists and a human rights lawyer have told the Associated Press (AP) news agency.

A Yemeni rights lawyer told the AP on Thursday that the women were rounded up from cafes and parks in the past months.

Speaking on condition of anonymity for fears for personal safety, he said families were still searching for their missing daughters.

The allegations were first raised over the weekend by the Yemen Organization for Combating Human Trafficking, based in the capital, Sanaa.

The group's founder, Nabil Fadel, said he had received information from families, former female detainees and other sources that, over the past months, the Houthis had been rounding up women over allegations of prostitution and collaboration with the Saudi-led coalition, which is at war with the rebels.

Fadel said that the arrests started after the Houthi appointment a year ago of Sultan Zabin as head of the Sanaa criminal investigation division.

Zabin promptly launched a crackdown on prostitution and smuggling. Women who had been rounded up in the crackdown and subsequently granted release were sent to secret detentions in villas across the Yemeni capital instead of being set free.

The rebel-run Interior Ministry responded to the allegations on Monday saying they were rumours from the "mouthpieces of the mercenaries" that are "tarnishing the image of security apparatus".

It also denied the existence of secret prisons and illegal and arbitrary detentions and vowed to prosecute those behind the reports.

The leader of the Houthis, Abdul-Malek al-Houthi, had recently warned in televised speeches about a so-called "soft war" against the Houthis by their enemies, pointing to their "corrupt morals and sins".

Smashed in their faces with batons

An AP investigation last month showed that thousands of Yemenis have been imprisoned by the Houthi militia during the four years of Yemen's grinding civil war.

Many of them suffered extreme torture, being smashed in their faces with batons, hung from chains by their wrists or genitals for weeks at a time, and scorched with acid.

The revelations about women detainees come as representatives of Yemen's warring sides are in Jordan for talks on implementing a prisoners exchange deal agreed to in Sweden last month.

In Sweden, the two sides agreed to confidence-building measures, including an exchange of thousands of prisoners, but the implementation of that has been slow marred by violence.

Yemen's war and ensuing economic collapse have unleashed the world's most urgent humanitarian crisis with more than 22 million people needing some kind of aid to survive.

The conflict erupted in 2014 when the rebels stormed south from their stronghold of Saada and overran much of the country, including the capital Sanaa where they overthrew the government of President Abd-Rabbu Mansour Hadi.

The situation escalated in 2015 when Saudi Arabia and the UAE, who accuse the Houthis of being Iranian proxies, formed a coalition that launched a massive air campaign aimed at reinstating Hadi's government.

With logistical support from the US, the coalition has carried out more than 18,000 raids on Houthi-held areas in an attempt to reverse their gains.

According to recent estimates, as many as 85,000 children may have died from hunger since the coalition's intervention.