The Houthis allegedly took control of Perim Island in the Bab el-Mandeb Strait and the city of Zubab in western Taiz province. An unnamed military source affiliated with Yemen's government made the claim.
As of 10:30 GMT, neither the Yemeni government nor the Houthis had issued an official statement on the claim.
The strategic importance of Bab el-Mandeb
Perim Island, also known in Arabic as Mayyun, lies in the middle of the Bab el-Mandeb Strait and divides the waterway into two channels. The strait, which connects the Red Sea with the Gulf of Aden, is among the key routes for international trade and energy shipments.
The Houthis were alleged to have gained an opportunity to complete their control over Bab el-Mandeb by taking control of Perim Island. The development involving control of Zubab and the island could increase regional and international concerns about the security of commercial vessels and energy tankers passing through the strait.
Claim that government forces withdrew to Lahij
The military source also said that Yemeni government forces withdrew to the southwestern province of Lahij after Zubab was seized. The Houthis' control of Zubab, a coastal city overlooking the Bab el-Mandeb Strait, was alleged to have strengthened their influence over the strategic waterway.
The Houthis previously entered the areas of Hays and al-Khawkhah and took control of the entire western province of Hudaydah. The Houthis then advanced in western Taiz, taking control of cities along the Red Sea coast, including Mokha, and expanding their access to the Bab el-Mandeb Strait through this advance.
Front lines in Yemen
Yemeni government forces were reported to be advancing in the northern province of Al Jawf and approaching its capital, Al Hazm. Fighting continued on the front lines in the provinces of Marib, Al Bayda and Al Dhale'e.
Conflict in Yemen has continued since the Houthis seized the capital, Sana'a, and parts of the country in September 2014. The Saudi-led Arab coalition intervened in March 2015 to support the internationally recognized government.