Backed by a Saudi-led Arab coalition, Yemeni troops launched an offensive last week to break the rebel siege on Yemen's flashpoint third city, in the country's southwest.
The heaviest fighting today was near its western entrance where air strikes by the Arab coalition and ground battles left 11 dead among Huthi rebels and their allies, loyalist military sources said.
An air raid killed two more rebels at the northern entrance to Taez, which has been encircled for more than year, the sources said.
"The blockade of Taez is almost broken after the retaking of Jabal al-Dhabab mountain" by loyalist forces, Colonel Abdulaziz al-Majidi, a spokesman of pro-government forces in the area, told AFP.
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"The road is now open between the west of Taez and southern provinces," he said, adding however that he was referring to a "rugged" route and not the main road.
The main road linking Taez to the south is still under rebel control.
Southern provinces are held by loyalist forces, while the rebels control the capital Sanaa, as well as the north and much of western Yemen.
Despite the latest loyalist advances, mines planted by the rebels around the city are so far hampering the delivery of much-needed humanitarian aid to Taez, according to military sources.
But dozens of residents have been using the sole open road, even before demining operations have been completed, to reach villages along the western outskirts, the sources added.
Yemen has been hit by unrest since the Huthi rebels and allied forces loyal to former president Ali Abdullah Saleh overran Sanaa in September 2014.
The UN says more than 6,600 people, mostly civilians, have since been killed and more than 80 percent of the population left in need of humanitarian aid.
The official sabanew.Net website reported today that local charities have distributed around 40 tonnes of food supplies funded by Qatari businessmen to some 1,000 families across Taez province.
In Saudi Arabia, where rebel attacks on the kingdom's side of the border intensified this month, civil defence authorities said three foreign residents were wounded today in shelling from Yemen on the city of Najran.