Three children were among those killed in clashes that have continued despite a ceasefire and peace talks in Kuwait between Huthi rebel and loyalist delegates, the sources said.
Another 13 civilians were wounded, the sources added, accusing the rebels of firing mortar and artillery rounds into the residential areas.
Rebel shelling of the besieged government garrison in Taez killed 11 civilians yesterday, drawing condemnation from UN envoy Ismail Ould Cheikh Ahmed.
However, the government sources in Taez said nine loyalist fighters were killed and 26 wounded in 24 hours of clashes in the city's eastern districts.
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Military sources told AFP that 12 rebels were also killed.
Witnesses said fighting continued today across several residential neighbourhoods of the southwestern city.
Separately, suspected jihadists attacked the airport in the government-held second city Aden, sparking a firefight that killed at least one civilian, a security source said.
Around 20 gunmen stormed the main entrance road to the airport in the city's Khormaksar district, demanding the release of a fellow jihadist of Western origin who was detained late last month.
The gunmen's leader told security forces he was a close relative of the detained jihadist, a Western national of Algerian origin.
The detained Westerner was among seven suspected members of the Islamic State group whose arrest was announced by the authorities in Aden on May 28.
Aden is the headquarters of the Saudi-backed government of President Abedrabbo Mansour Hadi since the capital Sanaa and swathes of the north and centre of the country are held by the Shiite Huthi rebels and their allies.