Reporter Hamdi al-Bokari, cameraman Abdulaziz al-Sabri and driver Munir al-Subaie went missing on January 18 while covering the conflict between rebels and Gulf-backed forces loyal to President Abedrabbo Mansour Hadi.
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The pan-Arab news channel said on its website early on Thursday morning that the three had been freed "a short while ago" after having been kidnapped by "unknown gunmen".
In a message posted on his Facebook page, Bokari said he had been held by the Iran-backed Shia Huthi rebels, under fire since March from a Saudi-led coalition, of which Qatar is a member.
"We heard them repeat 'Death to America'," a slogan the Huthis and Iranian protesters commonly chant, he wrote, adding that he would release more details about the kidnapping in the coming days.
The city of Taez is held by loyalists of Yemen's internationally recognised government, but it has been besieged by the Iran-backed rebels for months.
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The Huthis overran Sanaa more than a year ago, forcing Hadi's government to flee the Yemeni capital.
Hadi loyalists backed by a Saudi-led coalition have fought back and have been trying to retake Taez province and pave the way towards the rebel-held capital.
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