Fresh fighting between Houthis and government forces in Taiz

"Hospitals received six bodies, including two children, and 16 injured, including women, by the Houthi shelling," said Hasan Izzi, director of the health office in Taiz.

The rebel shelling comes just a week after pro-government forces broke through the siege of the city after months of blockade.

Hospitals were finally stocked up with medical supplies this week following a widespread deficiency.

"The hospitals received oxygen cylinders, medicines and other supplies, and they will receive more batches from Aden in the coming days."

Government-backed militias are still battling rebels in surrounding areas.

The news comes as Saudi Arabia promised to cut back its year-long offensive in Yemen.

Saudi Arabia and its coalition partners are set to scale down operations, but will continue to provide air support to Yemeni troops battling the Houthi rebels, said Saudi military spokesman, Brigadier-General Ahmed al-Asiri. 

"The aim of the coalition is to create a strong cohesive government with a strong national army and security forces that can combat terrorism and impose law and order across the country," Asiri told The Associated Press. 

Only "small" teams of coalition troops will remain on the ground to "equip, train and advise" Yemeni forces, al-Asiri said.

The coalition's primary task will be to help build a Yemeni army, he added.

These changes aim progressively to lead to a complete ceasefire and the gradual restoration of the political process in Yemen, sources told The New Arab.

Houthis captured Taiz - Yemen's third-largest city, located between the rebel-held capital, Sanaa, and the southern port city of Aden - several months ago, cutting off all roads and blocking humanitarian access for the estimated 200,000 residents.

More than 6,100 people have died - half of them civilians -since the Saudi-led coalition launched airstrikes on Yemen in March 2015, according to the United Nations.