The fighting, which has continued despite a cease-fire agreement, has resulted in the deaths of more than 20 people and the injury of some 80 others since last Thursday, Voice of America reported Wednesday.
Schools and hospitals are occupied or coming under attack by armed forces and armed groups, said Elizabeth Byrs of the U.N. Office for the Coordination of Humanitarian Affairs.
Hardest hit by the continuing violence are the city's children, the U.N. Children's Fund said.
UNICEF spokeswoman Marixie Mercado said the latest violence in Taiz has claimed the lives of three children and wounded seven others.
"That brings the total number of children killed so far to 138, the majority through live ammunition," Mercado said. "This includes bullets, shelling, missile attacks."
Mercado said the youngest victim to date was a 3-month-old infant.