Berkin Elvan spent nine months in a coma after being hit by a tear gas canister as he went to buy bread.
His death triggered more clashes with the police in over 30 towns and cities.
Recep Tayyip Erdogan’s comments could further inflame political tensions, correspondents say.
In a campaign speech ahead of local elections on March 30, Recep Tayyip Erdogan said the teenager was connected to “terrorist organizations”.
“This kid with steel marbles in his pockets, with a slingshot in his hand, his face covered with a scarf, who had been taken up into terror organizations, was unfortunately subjected to pepper gas,” he said in the speech broadcast on state TV.
Berkin Elvan’s funeral took place in Istanbul on Wednesday, providing a focus for further expressions of discontent with Recep Tayyip Erdogan.
Police fired water cannon and tear gas at protesters near Taksim Square, while his coffin was carried through the city’s streets.
Tens of thousands of mourners chanted anti-government slogans and Berkin Elvan’s mother accused Recep Tayyip Erdogan of killing her son.
Berkin Elvan’s death brought to at least eight the toll from last year’s unrest, including one policeman.
The protests began over plans to develop Istanbul’s Gezi Park into a new mosque and shopping centre, but escalated into national demonstrations against what opponents see as Recep Tayyip Erdogan’s growing authoritarianism.
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