The battles are raising fears of greater sectarian conflict, unseen for decades in Yemen.
Yemen has been chronically unstable for years. But its main fight has been by the government against al-Qaida militants who operate in the south and the mountainous center of the country.
In the past few months, however, the Shiite rebels known as the Hawthis have become one of the country's most powerful players.
Their main opponent has been Sunni Muslim hardliners, militias and army units allied with the Islah party, which is the Muslim Brotherhood's branch in Yemen, or tribal fighters sympathetic with the Brotherhood or al-Qaida.
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The government of President Abed Rabbo Mansour Hadi, an ally of the United States, appears largely caught in the middle between the two forces.
After taking control of the Sanaa suburb of Shamlan this week, Hawthi fighters yesterday launched an assault on the Sunni hardliners' stronghold, Iman University, which is seen as a breeding ground for militants.
"Every minute, there is something rattling or bombing, either rocket-propelled grenades or machine guns. The wall hangings fell down. The house was shaking with every explosion," Ammar Ahmed, who lives near the university, said of fighting overnight.
Army units joined Islah gunmen in fighting the rebels.
Bloodied bodies lay in the streets next the charred vehicles in front of the university, said another resident of the area, Ahmed Ibrahim. Hawthis tried to take a hill overlooking the university but were driven back by artillery fire, witnesses said.
At least 120 people, predominantly fighters from either side, were killed over the past 24 hours, according to medical officials, who spoke on condition of anonymity because they were not authorized to speak to the press.