"It is not surprising that the GCC rejects the constitutional declaration," Houthi group spokesman Mohamed Abdel-Salam said in a Facebook statement.
"There is nothing new about this [GCC] stance and the people of Yemen are aware that the positions of some of these countries are based on their political interests rather than the interest of vulnerable peoples," Abdel-Salam added.
He also stressed that the Houthis respect neighboring countries and "appreciate international relations that are based on mutual interest and respect."
On Saturday, the six-nation GCC rejected what it described as a "coup" Yemen's Shiite Houthi group staged against legitimacy in the poor Arab country.
It described the declaration as a step made in disregard for national, regional and international efforts seeking to maintain the security, stability and unity of Yemen.
In 2011, the GCC proposed an initiative to resolve Yemen's political crisis, which began after ex-President Ali Abdullah Saleh refused to step down on the heels of a popular uprising.
At the time, the initiative had called for the transfer of power in Yemen and the formation of a national accord government.
In recent months, however, Yemen has seen the emergence of a new political crisis – one that has left the Shiite Houthi group in control of capital Sanaa and certain other provinces.
Earlier this month, the Houthis announced a constitutional declaration with the stated aim of putting an end to Yemen's constitutional vacuum created by the resignation of President Abd Rabbuh Mansour Hadi.
The declaration dissolved Yemen's parliament and formed a "national council" to run Yemen during a two-year transition.