DUBAI, United Arab Emirates: Former Yemeni president Ali Abdullah Saleh has demanded the arrest of gunmen from the Houthi group suspected of killing one of his top associates last week.

The violence late Saturday between members of the Iran-aligned Houthis and Saleh loyalists marked strains within the main political coalition fighting the Saudi-backed government of President Abd-Rabbu Mansour Hadi in the 2-1/2-year civil war.

The killing of Colonel Khaled al-Radi, a senior member of Saleh's General People's Congress (GPC), was followed by a clash in the capital Sanaa in which two members of the Houthi group were also killed.

The Houthis and the GPC together rule northern Yemen and have maintained an uneasy alliance in a conflict that has killed at least 10,000 people and unleashed hunger and disease

Saleh ran Yemen for three decades. A mass rally to commemorate his party's founding anniversary last week angered Houthis, who viewed it as a show of force meant to undermine them.

Tensions boiled over two days later when Houthi fighters set up a security checkpoint near the home of Saleh's son, Salah, and his media office in Hadda district in southern Sanaa, where Radi was killed.

"He 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 ...," Saleh said in his speech, according to a transcript 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," Saleh told the crowd, referring to the Houthi-led government.

The two sides said on Tuesday they had agreed to ease tensions and allow investigators to probe the violence.

While the clashes have stopped, fighters from both sides remain deployed in back streets and in some buildings.

A Saudi-led coalition intervened in the war in 2015 in an effort to restore Hadi's government to power in Sanaa after the Houthis seized the capital and entered into alliance with Saleh.