Recep Tayyip Erdogan said Gezi Park was an issue "where we need to be courageous".
Plans envisaged rebuilding an old barracks and erecting other structures on the rare central green space.
Several people were killed and thousands injured in the protests which began in May 2013.
What started as demonstrations against urban redevelopment turned into a wider expression of anger against the policies of the government under Mr Erdogan, the then prime minister.
The excessive use of force by riot police escalated tensions.
"If we want to preserve our history we must rebuild this historic structure, we will rebuild it," he said in a speech in Istanbul, quoted by AFP news agency.
He was referring to the Ottoman-era barracks that used to stand in Gezi Park.
For some Turks, the proposed reconstruction of the barracks has symbolic significance. Some accounts say it was at the barracks that a failed mutiny by Islamic-minded soldiers was initiated in 1909.
The barracks were demolished in 1940, and attempts to rebuild them are seen by opponents to have the ring of Islamism.
In the wake of the 2013 unrest Turkey's top administrative court blocked the redevelopment but last year it reversed its decision, following an appeal by the municipality of Istanbul, AFP reports.
Turkey's president has signalled that he intends to revive plans to redevelop a central Istanbul park which sparked large anti-government protests in 2013.