The loyalists backed by warplanes of a Saudi-led military coalition took back areas in the western and southern suburbs of the city, said governor Ali al-Maamari.
They "reopened key roads that the Huthis (Iran-backed Shiite rebels) had been blocking for nine months," said the governor, who lives in exile in Saudi Arabia.
That should allow for humanitarian and medical aid to reach about 200,000 besieged inhabitants, he said.
Loyalist military sources said clashes between pro-government forces and air strikes had killed at least 57 people yesterday, 37 of them rebels, six civilians and the rest loyalist fighters.
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Dozens of military vehicles carried rebel fighters out of the western suburb of Taez towards the city of Hodeida on the Red Sea, witnesses said.
The coastal city remains under the control of the insurgents and their allies, army units loyal to former president Ali Abdullah Saleh.
Taez is located between the rebel-held capital Sanaa and the southern port city of Aden, which loyalists took back from the Huthis in July.
More than 6,100 people have died -- half of them civilians -- since the Saudi-led coalition launched airstrikes on Yemen in March 2015, according to the United Nations.