"Down, down with the Huthis' rule," chanted the protesters who rallied following a call by the Rejection Movement -- a group recently formed in provincial areas to challenge the powerful militia.
Dozens of Huthi supporters tried to stop the demonstration, triggering a brief scuffle, before they left, as the numbers of protesters kept increasing, an AFP correspondent reported.
Demonstrators gathered in Change Square near the University of Sanaa before they headed for Republican Palace, in central Sanaa, according to organisers.
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The palace is the residence of Prime Minister Khalid Bahah, who left it on Wednesday for an unknown destination after a two-day siege by the militia.
But the protesters changed their route and headed toward the residence of embattled President Abdrabuh Mansur Hadi to express their "rejection of his resignation," according to the organising committee.
The demonstrators were also demanding that Hadi "impose the authority of the state" in face of the tightening grip of Huthis on power, the organising committee said.
Hadi tendered his resignation Thursday saying he could no longer stay in office as the country was in "total deadlock".
Demonstrations also took off in the cities of Taez, Ibb and Hudaida, organisers said.