Several homes and a hospital were struck by mortar fire on Saturday.
The Shia group's advance on the capital has left scores dead this week and damaged many key buildings.
The showdown between the Houthis and forces loyal to the main Sunni party, Islah, has triggered Yemen's worst crisis since 2011.
The violence came as it emerged that a deal between the rival groups was under discussion.
One presidential source told a BBC Arabic correspondent in Sanaa that the Houthis - an armed Shia grouping - had signed a draft agreement proposed by President Abdrabbuh Mansour Hadi.
No confirmation was available, and details of any discussions were limited.
Much of the violence on Saturday was in the northern part of the capital, where the rebels tried to seize control of the Iman University from fighters loyal to Islah.
The capital's international airport remained closed for a second day. Hundreds have fled their homes.
Following serious clashes between armed groups on Thursday and Friday, hundreds of Yemenis have had to leave their homes. Many others are stranded in their houses unable to go out and buy food and supplies.
"Most of the neighbourhood has left and most shops have closed," says Samir al-Miqbaly, a small grocery owner near the headquarters of Yemen TV, the state broadcaster, where clashes have taken places for the past two days.
"The sounds of shelling are very strong and the fighting is so intense that we could feel our houses shaking."
Even in the relatively calm area of Hadda, one resident and mother-of-three is worried about sending her children to school next week.
"Where is the government in all of this?" she asks.
The Houthis, an armed Shia movement based in the mountainous northern province of Saada, have been advancing upon the capital for weeks, skirmishing with rivals and staging protests demanding political and economic reforms.
This week they attacked the offices of Islah and the headquarters of Yemen's state TV station. President Hadi has described the rebel offensive as a "coup attempt".
The Houthis, who belong to the minority Zaidi Shia community, have staged periodic uprisings since 2004 to win greater autonomy for Saada.
Yemen has remained unstable since an outbreak of anti-government protests in 2011, which forced the then-President Ali Abdallah Saleh from office.
Clashes between Yemen's Houthis and Sunni militias have continued in the capital, Sanaa, killing four people and leaving three hurt.