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Two Saudi Arabian religious teachers have arrived home after their release from more than nine months' detention by Houthi rebels in Yemen.

Abdulrahman al-Sharari and Salem al-Ghamdi landed in Riyadh on Thursday evening from Djibouti, the Saudi Press Agency said.

They were accompanied by the kingdom's ambassador to Yemen and UN envoy Ismail Ould Cheikh Ahmed who on Thursday finished a five-day mission to the rebel-held Yemeni capital Sanaa.

The teachers were on their way to work in the Comoros, on a flight which transited Sanaa, when air service was suspended at the start of a Saudi-led bombing campaign against the Houthi rebels on 26 March.

The teachers were staying at the United Nations mission in a local hotel but Houthis arrived and detained them until they were freed and handed over to Ould Cheikh Ahmed on Thursday.

In Sanaa, Ould Cheikh Ahmed met Houthi officials and others from the General People's Congress, the party of former president Ali Abdullah Saleh who is allied with the rebels.

The UN envoy said the rebels had taken positive steps during his visit, including the release of the Minister of Technological Education, Abdel Razzak al-Ashwal, a prominent member of the Al-Islah Sunni Islamist party.

Four other detainees, including activists and journalists, were also freed, he said.

He added that he received assurances about the condition of Defence Minister General Mahmud Sobeihi as well as Nasser Mansour Hadi, a brother of President Abedrabbo Mansour Hadi, and another general, Faisal Rajab.

Houthis captured them just before the coalition's intervention.

The liberation of the three men, and the lifting of a rebel siege on the city of Taiz, are among the demands of Hadi's government before a new round of peace talks can occur.

Ould Cheikh Ahmed had hoped to reach an agreement in Sanaa for a new round but he left Sanaa saying no date had been set.

The Saudi-led coalition is fighting in support of anti-rebel forces and Hadi's internationally backed government, in a war that has killed more than 5,800 people.

The UN says an estimated 80 percent of the population requires humanitarian aid.