"If official authorities do not assume their responsibilities, (we) will act to support the honourable people of Marib," Abdelmalek al-Huthi said in a televised address to supporters in Sanaa.
Yemen has been dogged by instability since an uprising forced longtime strongman Ali Abdullah Saleh from power in 2012, with Huthi rebels and Al-Qaeda seeking to fill the power vacuum.
The Huthis, also known as Ansarullah, overran the capital Sanaa unopposed in September and have since advanced into mainly Sunni districts.
Huthi accused "certain" tribesmen of wanting to hand over Marib to "Al-Qaeda and the takfiris," a reference to the Islamist Al-Islah movement that has fought alongside Al-Qaeda's Yemen franchise against the Shiite group.
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On Thursday Sunni tribesmen ambushed a military convoy travelling between Marib and Sanaa and seized heavy weapons they claimed were destined for Huthi militiamen, tribal sources and witnesses said.
Three soldiers died during ensuing clashes, according to Yemen's High Security Commission, which demanded in a statement late Friday the tribesmen return the military equipment they had seized.