Video footage uploaded to social media shows a group of men in suits punching and kicking the protesters.
Two people were arrested and 11 were injured, including a police officer, amid demonstrations Tuesday as Erdogan held meetings in the US capital after visiting President Donald Trump.
Witnesses told AFP that members of Erdogan's security detail pushed past Washington police outside the ambassador's residence and attacked a group of supporters of a Kurdish group.
Video footage uploaded to social media shows a group of men in suits punching and kicking the protesters, including a prone woman, as police struggle to contain the clash.
"Yesterday afternoon we witnessed what appeared to be a brutal attack on peaceful protesters outside the Turkish ambassador's residence," a police spokesman said.
"The actions seen outside the Turkish Embassy in Washington DC stand in contract to the First Amendment rights and principles we work tirelessly to protect every single day," a police statement said.
The First Amendment to the US Constitution protects the right of free expression.
The Metropolitan Police Department said it had arrested two people for assault and identified them as US residents, 49-year-old Ayten Necmi of New York and 42-year-old Jalal Kheirabadi of Virginia.
Social media posts by the two suspects suggest that Necmi is a supporter of Erdogan who came to Washington to celebrate his visit whereas Kheirabadi is a supporter of Kurdish causes.
But the police said they are also working with the US State Department and Secret Service "to identify and hold all suspects" -- suggesting that they are seeking to interview Erdogan's security detail.
The incident was very similar to another in Washington last year when Erdogan's guards roughed up Kurdish protesters outside the Brookings Institution think tank just before the president arrived to speak.