People were protesting against a power transfer deal that promises Ali Abdullah Saleh immunity from prosecution.
On Wednesday, Ali Abdullah Saleh signed the deal in Saudi Arabia under which he is to step down after more than 30 years in power.
Many other protesters were wounded in the clashes, reports say.
According to an AFP correspondent, the protesters were shot at by armed civilians whom they describe as Ali Abdullah Saleh’s “thugs”, as they marched towards the city centre.
At least four bodies taken from the scene of the shooting were visible at a nearby hospital, correspondents say.
Thousands of people in Sanaa cheered the news of Ali Abdullah Saleh’s impending departure, but others rejected the agreement.
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