The statement said: "The Dera al-Watan forces, the Giants Brigades, and the Joint Forces have established full control over the Kahboub front (part of the Bab al-Mandab region) as part of the Dawn of Yemen operations."
There was no immediate comment from the Houthi group regarding what the Dera al-Watan forces stated.
Kahboub, which is administratively located within Lahj Governorate (south), enjoys strategic importance as it includes a chain of commanding mountains overlooking the Bab al-Mandab Strait.
Fighting continues in Yemen between government forces and their allies on one side and the Houthis on the other on several fronts, on the third day of the "Dawn of Yemen" operation.
On Monday, the Chairman of the Yemeni Presidential Leadership Council, Rashad al-Alimi, announced the launch of the "Dawn of Yemen" operation, with the aim of "restoring state institutions, liberating the capital, Sanaa, and ending the Houthi coup."
Last July, a military escalation began in Yemen, the widest since the relative calm the country witnessed thanks to a truce that began in April 2022.
The pace of fighting accelerated last September, when the Houthis took control of vital sites in the governorates of Hodeidah and Taiz, including the strategic city of Mocha, reaching as far as Mayun Island overlooking the Bab al-Mandab Strait.
Yemen has been witnessing a war since the Houthis took control of the capital, Sanaa, and several governorates in September 2014, before an Arab coalition led by Saudi Arabia intervened in March 2015 in support of the Yemeni government.