They said the army also suffered casualties who were evacuated by helicopter but could give no figures.
The fighting broke out early on Monday in a suburb north of Taez that links the city of four million residents to the tribal areas around it, said the witnesses.
The tribesmen destroyed an army tank and took control of another as fighter jets overflew the area, they said.
Last week, a brief ceasefire between pro-opposition armed tribesmen and security forces had collapsed on Thursday when clashes resumed, leaving one policeman dead.
Tribesmen, who say their aim is to safeguard protesters who demand President Ali Abdullah Saleh stand down, have battled loyalist security forces for the past two months.
Saleh, who has been in power since 1978, has been receiving treatment in Saudi Arabia since early June for wounds sustained in a bomb blast at his palace.
Protesters have since January been calling for Saleh to quit office.
In a statement on Sunday, Saleh reiterated his appeal for dialogue in a statement for Yemenis on the beginning of the Muslim fasting month of Ramadan.
"There is no alternative to dialogue. This is the only way civilised people follow to achieve change and reform," he said in the message carried by state news agency Saba.
He urged all political forces in Yemen to abandon violence in the hope that Ramadan will return peace and stability to the country.
Saleh`s opponents have been calling for him to be prevented from returning to power.
On Saturday, influential Yemeni tribal leaders announced the creation of what they have named the "Alliance of Yemeni Tribes," a coalition to bolster six months of anti-Saleh protests. (M014/K004)
Editor: Kunto Wibisono
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