Ministers from Saudi Arabia, Kuwait, the UAE, Bahrain, Qatar and Oman made the appeal in a joint statement carried by the official Emirates News Agency on Tuesday.
The six "condemned the kidnapping of Emirati diplomat Naji al-Nuaimi and called on the Iraqi government to do everything in its power to put an end to his captivity".
The statement also reiterated the GCC's condemnation of "all forms of terrorism" and called for regional and international co-operation "to fight against terrorism with all means available in order to eradicate it".
The UAE's foreign minister and the Iraqi ambassador also met in Abu Dhabi to discuss the situation.
Al-Nuaimi was snatched last week while visiting his embassy's cultural annex in the upmarket Baghdad Sunni neighbourhood of al-Mansur by several kidnappers who burst into the building.
One of his Sudanese bodyguards, Bedawi Ahmed Ibrahim, was wounded in the assault.
On Thursday, the previously unknown Banner of Islam group claimed responsibility and called on Abu Dhabi to close its mission in the Iraqi capital within 24 hours.
It also demanded that Iraqi television station Al-Fayhah, which broadcasts from Dubai, be closed down.
The UAE on Friday recalled its charge d'affaires in Iraq.