A garrison loyal to President Abedrabbo Mansour Hadi has held out in the city largely surrounded by the Huthi rebels and their allies who control the capital Sanaa and much of the north.
Taez is one of the key battlegrounds of the civil war and government-held neighbourhoods have come under repeated rebel fire.
A medical source at the city's Al-Rawda hospital told AFP that seven civilians were also wounded by the rocket fire.
A loyalist military source said that the rockets struck one after the other in the city's Al-Nour district.
The United Nations has stepped up peace efforts this week with UN envoy Ismail Ould Cheikh Ahmed meeting Hadi at his base in second city Aden on Monday.
The envoy has been pushing a peace plan that would see a restored ceasefire leading to a political transition under which Hadi's powers would be significantly reduced.
The push for a negotiated settlement has been driven by mounting civilian casualties.
The World Health Organization says more than 7,400 people have been killed since the coalition intervention began. A UN spokesman has said the civilian death toll alone could top 10,000.
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