"The GCC states consider what happened in Sanaa on Tuesday, January 20, 2015 as a coup against the legitimate authority," the council said in a statement.
The council also pledged to send an envoy to Yemen in the event that Houthi rebels withdraw their forces from the presidential palace and other government buildings, remove their checkpoints and meet a number of security measures. The GCC secretary general is expected to meet all of the parties to the conflict.
Tensions in the country flared Saturday after Houthi fighters kidnapped Yemeni President Abd Rabbuh Mansur Hadi's chief of staff with two of his guards. Ongoing battles between government forces and fighters have subsequently been reported across Sanaa since early Monday.
Reports on Wednesday indicated that Shiite Houthi rebels had stormed and seized the presidential palace in Sanaa.
Yemen's central opposition movement, the Houthis were integral in ousting former President Ali Abdullah Saleh in 2012, overrunning the capital and taking over Yemen's western and central provinces.