The fighting erupted around Sanaa's central Saleh mosque, Yemen's largest, as Huthis tried to seize it ahead of tomorrow's celebration of the Prophet Mohammed's birthday, they said.
"The Huthis attempted to take control of the mosque in anticipation of a rally on Thursday" in the adjacent square, said an official from Saleh's General People's Congress, asking not to be named.
The mosque's guards, who were Saleh supporters, resisted, triggering a gunfight between the two camps, the GPC official said.
The official said four Saleh supporters were killed on the spot and a fifth died of his wounds later in hospital.
More From This Section
Nine Huthi fighters also died in the fighting, according to officials at two hospitals in the capital.
Rebel chief Abdulmalik al-Huthi had on Wednesday urged supporters across the country to head to Sanaa for the rally.
For decades sworn enemies, nationalist forces loyal to Saleh and the Iran-backed Shiite Huthis joined ranks in 2014 to drive the government of President Abedrabbo Mansour Hadi out of Sanaa.
That prompted a Saudi-led coalition to intervene the following year to prop up Hadi's government.
Despite a crippling coalition blockade, the Huthis and Saleh's forces continue to jointly control Sanaa, but tensions between them have escalated since a public dispute in August.
The Huthis accused Saleh of treason after the former president publicly dismissed the Iran-backed rebels as "militias".
Saleh's GPC party last month accused the Huthis of waging an "orchestrated campaign" against the former strongman and lacking "the will to maintain partnership".
The Huthis responded that the GPC had broken its pact by accepting funds from Hadi's government.