The Turkish leader on Tuesday negotiated what could have been a fraught White House encounter with President Donald Trump with some success but, as he pursued his Washington visit, chaos erupted.
Erdogan has been caught on tape by Voice of America, watching the incident.
Erdogan then gets out of the vehicle, and starts to watch how his security detail beats the protesters, while the first bodyguard returns to him, as if briefing on the happening.
Close-up footage shared on social media showed Turkish officials dressed in suits beating and punching people in the crowd and, in at least one case, kicking out at a woman splayed on the ground. "The American police let them attack us".
The State Department said Wednesday that "violence is never an appropriate response to free speech, and we support the rights of people everywhere to free expression and peaceful protest".
"We are communicating our concern to the Turkish government in the strongest possible terms".
Lawsuits can also be sought, said McCain, as "we can identify these people", but the first step should be to throw the ambassador out of the United States.
Several other Senate Republicans, including Marco Rubio of Florida and Ted Cruz of Texas, called on the Turkish government to immediately apologize for the violence.
Sen. Patrick Leahy's tweet said "We've got to come back to American values".
According to D.C. Police Chief Peter Newsham, the situation was especially "dicey" because some of the Turkish guards were armed.
Speaking in Istanbul two days after meeting President Donald Trump in Washington, Erdogan criticised the USA decision to ally with "terror organisations" for the long-awaited operation to capture Raqqa, the de facto capital of IS.
But the Turkish Embassy said the demonstrators were aggressively provoking Turkish-Americans who had gathered to greet the president, and they in turn responded in self-defence.
A violent attack blocks from the White House that left nine protestors bloodied or injured is creating a new headache for the Trump administration on the eve of the president's first foreign trip.
House Foreign Affairs Committee Chairman Ed Royce also sent a letter to Attorney General Jeff Sessions and Secretary of State Rex Tillerson urging them to take action over the clashes.
"Alarmingly, this behavior is indicative of the broad crackdowns on political activists, journalists and religious freedom in Turkey that have greatly harmed Turkish democracy in recent years", Royce wrote.
Pursuing charges would also threaten to further inflame the uneasy relationship between the United States and its North Atlantic Treaty Organisation ally.
Because "police did not heed Turkish demands to intervene", Erdogan's security team and Turkish citizens moved in and "dispersed them", the news agency said.
"Just past year, when Erdogan was back in the States for a summit on nuclear security, at Brookings, outside Brookings, [in Washington, D.C.], there were similar protests and similar unseemly scenes of clashes along Massachusetts Avenue".