Security sources close to Saleh said armed supporters of the Huthis had surrounded the residences of local officials in the rebel government who are linked to the former president.
Saleh loyalists were also seen taking up positions in the streets of the rebel-controlled city, witnesses and a security source there said.
Saleh and the Huthis forged an unlikely alliance in 2014, ending decades of animosity to join ranks in fighting against Yemen's internationally recognised government.
Today's violence comes 24 hours after clashes at the Saleh mosque in Sanaa late yesterday killed nine Huthi rebels and five Saleh supporters, according to multiple medical sources at hospitals in the capital.
One source at the Jumhuriya hospital today said the death toll had risen to as many as 18 rebels and six Saleh loyalists. The numbers could not be confirmed by other hospitals in the area.
The latest clashes erupted hours after tens of thousands of Yemenis packed Sanaa's Sabaeen Square to mark the Prophet Mohammed's birthday, heeding a call from rebel chief Abdul Malik al-Huthi.
A source in Saleh's forces said Huthi fighters were positioned around the residences of two of the ex-president's nephews.
Also in the day, the Huthis, who are backed by Iran, said they fired a ballistic missile at Saudi Arabia and hit a military target, in the second such attack this month, after threatening to retaliate over a crippling blockade.
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