Medical officials said 24 tribesmen were killed in on Tuesday's clashes. Government officials put the death toll among soldiers at 14, and 20 were missing.
As the battles developed, the heart of Yemen's capital was turned into a no man's land with heavy gunfire, mortar rounds and artillery fire from government forces. As the death toll mounted, Saleh called for a cease-fire.
Both sides traded blame for triggering the latest violence, further deepening the rifts and suggesting Yemen could be stumbling toward a potentially bloody showdown between well-armed tribal militias and pro-Saleh troops.
A statement by opposition groups accused Saleh of "dragging the country to chaos." The Interior Ministry, in turn, blamed the "bloodshed" on Sheik Sadeq al-Ahmar, the head of Yemen's largest tribe, called the Hashid.
Saleh has refused to step down despite three months of nearly nonstop protests calling for an end to his 32-year rule. He also snubbed attempts by Arab neighbours to negotiate his exit.