They insisted after a meeting in Riyadh that the talks be held in Saudi Arabia, which leads an Arab coalition that has been bombing the Shiite rebels since late March.
Iran has proposed holding United Nations talks on ending the war in Yemen at a neutral venue, excluding all countries from the coalition.
But in a statement after talks at a Riyadh airbase the six Gulf Cooperation Council states "affirmed their support to intensive efforts by the legitimate Yemeni government to hold a conference under the umbrella of the GCC secretariat in Riyadh."
The GCC groups regional heavyweight Saudi Arabia along with Bahrain, Kuwait, Oman, Qatar, and the United Arab Emirates.
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All but Oman belong to the coalition, although Western diplomats have said Saudi Arabia carried out the majority of strikes against the Huthis itself.
Coalition warplanes pressed their attacks on rebel positions as the ministers met for about three hours in a chandeliered room.
The air strikes began in late March when the Huthis and their allies advanced on the main southern city of Aden, where President Abedrabbo Mansour Hadi fled after the rebels seized large parts of the country including Sanaa.
Iran has denied charges of arming the rebels, called for an end to the strikes and pushed for a negotiated settlement.
The conflict has heightened tensions in the region.
Iran said two of its destroyers sent to the Gulf of Aden had reached the entrance of Bab al-Mandab, a strategic strait between Yemen and Djibouti.
Tehran stressed the warships would stay out of the territorial waters of other countries.
The coalition has imposed an air and sea blockade on Yemen.
Last week US officials said an American aircraft carrier and a cruiser left the waters off Yemen and headed back to the Gulf after an Iranian naval convoy also turned back from the area.