Former Yemeni president Ali Abdullah Saleh has demanded the arrest of Houthi gunmen suspected of killing one of his top associates last week.
The violence late on Saturday between members of the Iran-backed Houthi rebels and Saleh loyalists marked strains within the main political and military coalition fighting the government of president Abdrabu Mansur Hadi.
The killing of Colonel Khaled Al Radi, a senior member of Mr Saleh's General People's Congress (GPC) party, was followed by a clash in the capital, Sanaa, in which two Houthis were also killed.
The rebel movement and the GPC rule northern Yemen as part of a political coalition and have maintained an uneasy alliance in a conflict that has killed at least 10,000 people.
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Mr Saleh ran Yemen for three decades. A mass rally to commemorate his party's founding anniversary last week angered the Houthis, who viewed it as a show of force meant to undermine them. Earlier in the week the rebels had issued a ban on such "partisan" activities.
Tensions boiled over two days later when Houthi fighters set up a security checkpoint near the home of Mr Saleh's son Salah and his media office in the Hadda district of southern Sanaa, where Radi was killed.
"He (Radi) stopped to see the commotion, when my son Salah had been stopped and searched and they (checkpoint guards) demanded his weapons and his ID card," Mr Saleh said in a speech, the transcript for which was published on the GPC's website.
He said his son left the scene in a vehicle, while Radi, who was standing on the sidewalk, was shot dead.
"The political leadership … must take responsibility and accelerate the investigations and the arrest of the perpetrators and bring them to justice," Mr Saleh said, referring to the Houthi-led administration running Sanaa.
The two sides said on Tuesday they had agreed to ease tensions and allow investigators to probe the violence.
Although the clashes have stopped, fighters from both sides remain deployed in backstreets and in some buildings of the capital.
A Saudi-led coalition that includes the UAE intervened in Yemen's war in March 2015 in an effort to restore Mr Hadi's government to power in Sanaa after the Houthis seized the capital and entered into the alliance with Mr Saleh and his supporters.