With Yemen sinking more and more into turmoil, the GCC called on Saleh on Sunday to step down as part of a deal with the protest movement demanding his ouster after 32 years.
The GCC did not specify a time frame for a transfer of power from Saleh to his deputy.
Saleh's response Monday came in a statement from the presidential palace, stressing that the president "has repeatedly expressed no reservations to the peaceful and easy transfer of power within the constitution," which allows him to remain in office until the 2013 elections.
It said the GCC offer was a "basis for dialogue that will enable the country to avoid the misfortunes of chaos, destruction, disruption of security and public order and social peace."
Saleh's supporters and pro-government groups went beyond the president's carefully worded statement, rejecting the GCC offer as a "flagrant interference in Yemen's internal issues." According to the official SABA news agency, the groups denounced the GCC and said their move "goes against the will of the Yemeni people."
The anti-government protesters, on the other hand, insisted Monday that Saleh step down and that he and his family members be put on trial.
Wassim Al-Qarshi, an organizer of the daily protests in the capital Sanaa said the "people are determined to continue their protests in the public squares until their demands are achieved."
Keeping up the pressure, tens of thousands of protesters took to the streets Monday in the country's major cities, pushing for Saleh to go. In Sanaa, the demonstrators included a considerable number of women. There were also marches in the main streets of Taiz, Aden and elsewhere.
In a separate development, 11 suspected Al-Qaeda members were killed in a clash with Yemeni forces on Monday in the south of the country. Two of the militants killed in the clashes in Abyan province were foreigners, the official website of the Defense Ministry said.
