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"The correct step to preserve the GCC would be to freeze Qatar's membership until it sees reason and accepts the demands of our countries. If not, we will be fine with it leaving the GCC," Sheikh Khalid bin Ahmed Al Khalifa said on Twitter.
Bahrain, Saudi Arabia, the United Arab Emirates and Egypt on June 5 severed ties with Qatar over accusations of supporting extremism and being too close to Iran, charges Doha has denied.
Founded in 1981, the GCC is a political and economic union that includes Saudi Arabia, Bahrain, the United Arab Emirates and Qatar, as well as Oman and Kuwait.
Experts have warned that the nearly five-month-long diplomatic crisis could cause the six-nation bloc's demise.
Saudi Arabia and its allies in June issued Qatar with a list of demands, including shutting down Doha-based broadcaster Al Jazeera, curbing relations with Iran and closing a Turkish military base in the emirate.
"Bahrain will not attend a summit with Qatar, which becomes closer to Iran each day and brings foreign forces (to its soil), dangerous steps for the security of GCC countries," Sheikh Khalid said.
GCC members are supposed to meet before the end of the year, but the crisis could see the bloc's annual meeting postponed or cancelled.
After severing ties with Doha, Riyadh and its allies closed land and maritime borders, and suspended air links.
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