The fighting in Taiz comes despite a five-day humanitarian truce which began on Tuesday to distribute aid to the millions deprived of food, fuel and medicine by weeks of fighting.
Saudi Arabia, leading a coalition of Arab states backed by the West, has pounded Iranian-allied Houthi forces and fighters loyal to Yemen's former leader Ali Abdullah Saleh since March 26, aiming to restore President Abd-Rabbu Mansour Hadi.
Some fighting also took place in the city of Dhalea on Saturday night but there was no immediate information on casualties.
A conference between Yemeni political groups has been scheduled by President Hadi's government for Monday in Riyadh after the ceasefire ends.
The conference was rejected by both the Houthis and fighters loyal to former president Saleh, meaning it will not provide an opportunity for peace talks.
However, some leading figures from Saleh's political party, the General People's Congress (GPC), have gone to Riyadh and pledged loyalty to Hadi's government.Those figures issued a statement late on Saturday asking for Saleh to step down as president of the GPC and declared they would take part in the Riyadh talks.