The Huthis, whose militiamen seized Sanaa in September, vowed to take further "revolutionary steps" following yesterday's blasts.
The Islamic State (IS) group claimed responsibility for the attacks on two mosques in the capital Sanaa and another in the Huthi's northern stronghold of Saada.
They were the first claimed by IS in Yemen, where rival Al-Qaeda has traditionally been the dominant jihadist outfit.
President Abedrabbo Mansour Hadi has taken refuge in the southern city of Aden having escaped house arrest in the Huthi-controlled capital last month.
More From This Section
"Such heinous attacks could only be done by the enemies of life," who want to drag Yemen into "chaos, violence and internal fighting," said the letter released by his office late yesterday.
"Shiite extremism, represented by the armed Huthi militia, and Sunni extremism, represented by Al-Qaeda, are two sides of the same coin, who do not wish good and stability for Yemen and its people," Hadi wrote.
Hadi has declared Aden the temporary capital of Yemen.
There were signs that security forces allied with the Huthis and former president Ali Abdullah Saleh were planning to seize Taez - a strategic city between the capital and Aden.
Since taking over Sanaa the Huthis have tightened their grip on government institutions, aided by forces loyal to former strongman Saleh.
In their push to widen their control to the south, they have faced fierce resistance by Sunni tribes allied with Al-Qaeda militants who are active in the impoverished country.
In an online statement claiming responsibility, the Sanaa branch of IS said the attacks were "just the tip of the iceberg".