Khaled al-Jarallah said on Wednesday that Kuwait aims to continue its role as an active member of the council and will do so by hosting a lawmakers' conference in which senior legislators from the six Gulf countries would convene.
"The working mechanism of the GCC will not be frozen or impeded due to a conviction that whatever the magnitude of the dispute, it should be avoided," said al-Jarallah, according to Kuwait's state news agency KUNA.
His remarks come as an ongoing diplomatic crisis in the region is in its seventh month.
Since June, Saudi Arabia, Bahrain, the United Arab Emirates (UAE) and Egypt have enforced a land, sea and air blockade against Qatar, accusing the tiny Gulf nation of supporting "terrorism".
Qatar has denied the allegations and accused the neighbouring countries of attempting to infringe on its sovereignty.
"A breakthrough will be reached someday … mediation efforts will not stop," al-Jarallah said.
Earlier this month, the 38th GCC summit in Kuwait City was cut short by one day.
The move came as the UAE announced that it had formed a new economic and military partnership with Saudi Arabia, separate from the GCC.
The council was established in 1981 to foster closer economic, trade and security partnerships on the Arabian Peninsula.
According to KUNA, parliament speaker Marzouq al-Ghanim said the upcoming two-day lawmakers' conference would be instrumental in restoring a sense of normality amid the ongoing rift.
The conference, scheduled to start on January 8, is expected to take place under the auspices of Kuwaiti Emir Sheikh Sabah al-Ahmad Al Sabah, who has been mediating the standoff.
He previously warned of the potential collapse of the GCC if the crisis continued.
Following last month's GCC summit, the Kuwaiti leader said the structure of the six-member council would have to change in the near future to face upcoming challenges.
"We might change the system of the GCC to have mechanisms to better face challenges," he said at the time.