The clashes have eliminated hope of the warring parties abiding by a truce announced by US Secretary of State John Kerry that was to have taken effect yesterday.
Loyalist military sources told AFP that 13 rebels and eight pro-government forces were killed over the past 24 hours, while the rebels reported dozens of casualties in shelling of a local market.
Two civilians were also killed and 16 wounded as rebels fired Katyusha rockets on a residential area of Taez, they said.
A rocket crashed into a market selling the mild narcotic leaf qat, popular among Yemenis, leaving 40 casualties, said sabanews.Net, without giving a breakdown of dead and wounded.
The medical charity Doctors Without Borders (MSF) said emergency rooms it supports or manages in Taez province had received a total of 21 dead and 76 wounded.
Among those killed was a watchman who works at the MSF trauma centre in Taez.
He was killed while "off duty when a blast hit a local market in the neighbourhood", said Djoen Besselink, who heads the MSF mission in Yemen.
Pro-government forces are pressing on with a four-day-old offensive to recapture the presidential residence and police headquarters in the southwestern city, while the Shiite Huthi rebels have brought in reinforcements.
The fighting continued despite Kerry's announcement of a new ceasefire.
The US chief diplomat said on Tuesday that rebels were ready to observe a ceasefire plan taking effect from November 17, but President Abedrabbo Mansour Hadi's government said it was not aware of any new peace initiative.
A Saudi-led coalition which is backing Hadi's internationally recognised government told AFP Thursday that "until now there is no demand from the legitimate government (of Yemen) to observe a ceasefire," adding that operations will continue.
The UN says more than 7,000 people have been killed and nearly 37,000 wounded in Yemen since the Arab coalition launched a military campaign in March 2015.
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