The GCC is a six-nation bloc that groups Saudi Arabia, the United Arab Emirates, Bahrain, Kuwait, Qatar and Oman.
Ties have been tense between Iran and GCC members Saudi Arabia and the UAEnited Arab Emirates, both allies of the United States and leading members of a military coalition battling Iran-backed Huthi rebels in Yemen.
In September, Rouhani proposed in a speech at the UN General Assembly a "Coalition for Hope" that would unite all regional countries in a pledge of non-aggression and non-interference in each others' affairs.
It came after a string of mysterious attacks on oil tankers in the Gulf and Saudi oil installations, which the United States blamed on Tehran. Iran denied any involvement in the attacks.
"The security of the region shall be provided when American troops pull out," Rouhani said at the General Assembly.
"In the event of an incident, you and we shall not remain alone. We are neighbours with each other and not with the United States," he added.
Tensions between Tehran and Washington have escalated sharply since US President Donald Trump unilaterally withdrew last year from the 2015 Iran nuclear deal.
He has since reimposed unilateral sanctions as part of its "maximum pressure" campaign.
The arch-foes came to the brink of a military confrontation in June when Iran downed a US drone and Trump ordered retaliatory strikes before cancelling them at the last minute.