"This historic and responsible initiative is in the interest of the country... Because it fills a political vacuum," Abdel Malek al-Huthi said in a televised address to his supporters gathered in a northern Sanaa stadium.
He said it was "in the interest of all Yemenis without exception", including the separatists of southern Yemen.
The formation of the council, announced on Friday, would also head off the threat from Al-Qaeda which has a strong presence in east and south Yemen, Huthi said.
Yemen's Gulf neighbours today condemned the moves by the Shiite militia, named Huthis after their leadership, and said they "totally undermine" international and regional efforts to help resolve the impoverished country's crisis.
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"The Huthi coup marks a grave and unacceptable escalation... And endangers the security, stability, sovereignty and territorial integrity of Yemen," said the Saudi-led Gulf Cooperation Council (GCC).
The six Sunni monarchies said their own security was linked to that of their neighbour Yemen, and vowed to take "all the necessary measures to defend their interests", without elaborating.
Influential tribal leaders in the oil-rich eastern province of Marib have said they "rejected the authors of this coup".
And a US official at a security conference in Munich said Washington and its GCC allies "don't agree" with the Huthi "presidential council".
UN Security Council president Liu Jieyi said its 15 members were ready to "take further steps" if UN-brokered negotiations to resolve Yemen's political crisis were not resumed "immediately".