The clashes came after UN envoy Ismail Ould Cheikh Ahmed flew out of the rebel-held capital of Sanaa yesterday without securing agreement on a ceasefire for the Muslim holy month of Ramadan which begins this weekend.
The government garrison in Taez is almost completely surrounded by Shiite Huthi rebels and their allies, and the city has come under repeated bombardment.
Security officials named the dead men as Takieddin Hutheifi and Wael al-Abassi. Two other cameramen were wounded.
The rebels overran Sanaa in September 2014 and then seized much of the rest of Yemen, prompting President Abedrabbo Mansour Hadi to flee to neighbouring Saudi Arabia in March 2015.
The support of a Saudi-led military coalition has enabled Hadi loyalists to retake the south of the country but most of the north and the Red Sea coast remain in rebel hands.