"President Trump called me about a week ago about this issue. He said that he was sorry, and he told me that he was going to follow up on this issue when we come to the United States within the framework of an official visit," the Turkish leader said.
The White House, however, has denied that the US president had said he was "sorry" for the brawl.
"They discussed a wide range of issues but there was no apology," a White House official told US broadcaster CNBC.
The clash between Kurdish protesters and President Erdogan's security team took place in May, during the Turkish head of state's visit to Washington.
Video footage of the clash shows Erdogan's bodyguards beating protesters while US police struggle to break up the scuffle.
Following the incident, 15 Turkish security guards were indicted by a grand jury in Washington over what the state's police chief described as a "brutal attack" on protesters.
