There has been no official word on casualties but the International Committee of the Red Cross (ICRC) said that dozens were killed and hundreds were wounded in the fighting.
Khattar Abou Diab, who teaches political science at the University of Paris, tells VOA that former president Saleh has a "strong political instinct" and that he made his move against the Houthis at a time when the situation on the ground is favorable.
The United Nations released a stern warning on Friday to the Saudi-led coalition of the catastrophic consequences associated with not fully lifting the blockade on Yemen, and UN leaders on Saturday issued a joint statement calling for the full lifting of the blockade. "Should the blockade continue, we know what (targets) would cause great pain and how to reach them", he said in a speech broadcast on Al-Masira.
The comments, carried by the Saudi-owned Al-Hadath news channel, came after Saleh said he was ready to turn a new page with the coalition if it stopped what he described as its aggression on Yemen and lifted restrictions on transportation.
The Houthi chief also accused Saleh of secret collaboration with the leaders of the coalition.
The Saudi-led coalition, consisting of several Arab-Sunni states, intervened in neighbouring Yemen to push back Houthi rebels and has since been trying to reinstate the government of President Abd-Rabbu Mansour Hadi.
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The Houthis accused Mr Saleh of betrayal, and vowed to keep up the fight against the Saudi-led coalition. "The priority has been and still is to confront the forces of aggression".
However, in a statement, Saleh's party, the GPC, ordered their supporters to defy Houthi's orders and to "defend their homeland, their revolution, and their unity".
Meanwhile, Houthi leader, Abdel-Malek al-Houthi, called for dialogue with Saleh and his rebel forces to end the growing violence between the two factions.
A statement from Saleh's General People's Congress Party said three guards were killed when Houthi forces attacked the house of Tarek Saleh, Ali Abdullah Saleh's nephew, adding that they also besieged the residence of Ibrahim Sharaf, a party member and foreign minister of the Sanaa-based government.
"The GPC appealed to the army and security forces to remain neutral in the conflict".
In March 2015, warplanes from Saudi Arabia, the UAE, Kuwait, Bahrain, Qatar and other allies began airstrikes on rebel positions in Yemen.