Sunday's statement comes after the Lebanon-based TV station Al-Mayadeen reported that Qatar gave Hamas a list of leaders who should leave.
Qatari officials did not respond to a request for comment. Its state-run Qatar News Agency has been offline since an alleged hack in May that reignited tensions between the gas-rich nation and its Gulf Arab neighbors over its support of Islamist groups.
Hamas noted in its statement that the Palestinian group's leadership is now based in the Gaza Strip, after Gaza native Ismail Haniyeh replaced Qatar-based Khaled Mashaal as the top leader in recent elections.
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