The GSF, which is seeking to break Israel's naval blockade and deliver humanitarian aid to war-torn Gaza using civilian boats, said in a statement on Wednesday all passengers and crew were unharmed.
GSF reported the first attack on Tuesday saying one of its vessels had been struck by a drone in Tunisian waters, reports Tunisian authorities said were false.
A Tunisian Coast Guard spokesperson did not respond to a call from Reuters.
The flotilla posted a video on Instagram of the alleged attack, showing a luminous object hitting the boat and fire erupting immediately afterwards on board. Reuters was not immediately able to verify the video.
The group said the British-flagged Alma sustained fire damage to its top deck and an investigation was underway.
Several ambulances rushed to the port, while a Reuters witness reported coastguard boats near the Alma.
The flotilla is supported by delegations from 44 countries, including Swedish activist Greta Thunberg and Portuguese left-wing politician Mariana Mortagua.
Israel has maintained the blockade on the coastal enclave since Hamas seized control of Gaza in 2007, saying it is needed to prevent weapons smuggling.
The blockade has remained in place through the current war, which began when Hamas attacked southern Israel in October 2023, killing 1200 and taking about 250 hostages, Israeli tallies showed.
Israel's subsequent military assault against Hamas has killed over 64,000 Palestinians, Gaza's health ministry said, while a global hunger monitor said part of the enclave is suffering from famine.
Israel sealed off Gaza by land in early March, letting in no supplies for three months and sparking the widespread shortage of food. It has said Hamas was diverting the aid.
In June, Israeli naval forces boarded and seized a British-flagged yacht carrying Thunberg, among others. Israel dismissed the aid ship as a propaganda stunt in support of Hamas.
The GSF statement did not say who it believed was behind the alleged attacks, but described them as an "orchestrated attempt to distract and derail our mission".
"The Global Sumud Flotilla continues undeterred. Our peaceful voyage to break Israel's illegal siege on Gaza and stand in unwavering solidarity with its people presses forward with determination and resolve," the group added.
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