The Huthis -- also known as Ansarullah -- have advanced out of their northern mountain strongholds towards Sanaa in a suspected attempt to expand their sphere of influence as Yemen is reorganised into six regions.
"Armed militants belonging to the Ansarullah Huthi (rebels) opened fire at security patrols carrying out their duties in the capital" yesterday, state news agency Saba said.
Militants blocked a road in Sanaa's Al-Jarraf district, where the rebels have a representative office near the interior ministry, and fired on police patrols from surrounding buildings.
Security officials told AFP the incident took place after authorities arrested two wanted rebels and tried to detain others.
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Ansarullah said in a statement security forces "targeted" the rebels' Sanaa office to "ignite a meaningless war".
Yesterday hundreds of Yemenis protested outside the presidential residence over what they say is the authorities' inaction over the rebel advance.
Fighting between troops and rebels neared Sanaa on Friday, with clashes reaching the town of Bani Matar, only 15 kilometres (nine miles) northwest of the capital, tribal and security sources said.
The sources said that "dozens" have been killed, but were unable to provide a precise toll.
A new round of clashes with rebels erupted in Yemen's north a week ago, ending an 11-day truce agreed after mediation backed by United Nations envoy Jamal Benomar.
Huthis have been battling the central government for years from their Saada heartland, complaining of marginalisation under former president Ali Abdullah Saleh, who stepped down in 2012 after a year-long uprising.