Houthis cut off a main road used to get daily humanitarian needs into Taiz city, the new frontline between the rebels and Yemeni forces, Sky News Arabia reported on Thursday.
For months, Yemeni forces affiliated to the legitimate government, backed by the Saudi Arabia-led Arab coalition, have been battling Houthis and pro-Saleh forces for control of Taiz for months.
Meanwhile, unidentified armed men threw a hand bomb at the Yemeni Foreign Ministry headquarters in Aden city.
No casualties were reported.
In the meantime, Houthis shelled a number of Taiz's districts in which blasts rocked the city.
At least 5,700 people have been killed, almost half of them civilians, since the conflict in Yemen escalated in March, when the coalition launched an air campaign after the Houthis forced President Abdrabbuh Mansour Hadi to flee the country.