And new video revealed Thursday shows Erdogan - who hours earlier had met with President Donald Trump - watching the fracas from his auto outside the Turkish embassy. "There is no excuse for this kind of thuggish behavior", McCain initially tweeted after the incident.
"This kind of thing cannot go unresponded to diplomatically", he said, adding that legal action could be pursued.
The protest group included Armenian and Kurdish activists opposed to Erdogan, two of whom were arrested in the immediate aftermath.
Washington and Ankara are bitterly at odds over United States support for the Kurdish People's Protection Units (YPG) in Syria, a group that Turkey considers a front for banned Kurdistan Workers' Party (PKK) separatists.
And while State also confirmed that two members of the Turkish president's security team were detained after the attacks, they were soon released on diplomatic immunity grounds. The aide was not authorized to speak publicly and spoke on condition of anonymity.
A firebrand U.S. senator has advocated for Turkey's Ambassador Serdar Kilic's removal of diplomatic credentials after what he called "thuggish" clashes in front of the Turkish embassy in the United States capital.
Also on Wednesday, chairman of the House Foreign Affairs Committee, Rep. Ed Royce, R-Calif., sent a letter to Attorney General Jeff Sessions and Secretary of State Rex Tillerson on Wednesday urging immediate action to hold individuals accountable. "And I thought, 'okay I'm on the ground already, what is the objective to beat me?'"More news: Ohio unemployment rate inches down to 5 percent for April
As the violence broke out, videos from the confrontation quickly spread on social media showing Erdogan's bodyguards pummeling people, even kicking people in the face.
Tuesday's fight outside the embassy injured 11 people, at least one critically. The State Department condemned the attack as an assault on free speech, issuing a statement to express its concern regarding the violence outside the Turkish ambassador's residence.
An embassy statement said the group had "aggressively provoked Turkish-American citizens" who had gathered to greet Erdogan.
"The Turkish-Americans responded in self-defense", the statement said. That Mr.Erdogan has unfortunately been successful in stifling dissent in Turkey doesn't give him license to come to this country and attack one of its most basic, and cherished, freedoms.
The decision is meant to accelerate the operation to recapture the key Islamic State group stronghold of Raqqa.
Turkey considers the People's Protection Units or YPG in Syria a terror organization an extension of the Kurdistan Workers' Party (PKK) which has waged a three-decade long insurgency against the Turkish state, seeking their own nation.