Nine people were hospitalized after the encounter.
Both pro- and anti-Erdogan groups had gathered outside the embassy Tuesday.
The US police also branded the incident as a "brutal attack" on peaceful protesters.
The new video obtained by Voice of America shows the driveway of the Turkish ambassador's residence, where Mr Erdogan is seated in the back of a black Mercedes, as protesters chant outside. They "began aggressively provoking Turkish-American citizens who had peacefully assembled to greet the President".
A State Department spokeswoman said, referring to the incident, the United States is communicating concerns to Turkey's government "in strongest possible terms".
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Macron also called on the European Union to toughen its policies against countries that flout the rules of global trade. Merkel admitted on Monday that, "as things are looking at the moment, we will not reach this goal".
The minister said Trump's new USA administration seems more understanding about Turkey's security concerns.
And Erdogan, speaking in Istanbul two days after meeting Trump, said he was putting Washington on notice that his forces won't hesitate to attack USA -backed Kurds if they threaten Turkey.
Two men were also arrested by D.C.'s Metropolitan Police Department on the scene - Jalal Kheirabaoi of Fairfax, VA, and Ayten Necmi of Woodside, NY, according to police reports.
Although the PKK is recognised as a terrorist organisation by Turkey, the United States and the European Union, their supporters are usually not arrested in western countries in the same manner that sympathisers of Daesh, another terrorist organisation, routinely are.
The United States is expressing concern over a clash involving protesters and supporters of Turkish President Recep Tayyip Erdogan.
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Longtime Macron supporter and campaign manager Richard Ferrand was rewarded with the territorial cohesion portfolio. The biggest surprise was the appointment of television star and environmentalist Nicolas Hulot as ecology minister.
He warned that Brett McGurk, the United States diplomatic envoy to the Operation Inherent Resolve coalition, should not "poison" the administration by backing Kurdish groups in a continuation of Obama-era policies.
"We intend to ensure accountability of anybody involved", said DC police chief Peter Newsham of the situation.
Turkish President Recep Tayyip Erdogan, whose name Donald Trump doesn't know how to pronounce, met with POTUS in Washington on Tuesday, presumably to swap stories about their mutual friend Michael Flynn.
House of Representatives Foreign Affairs Committee Chairman Ed Royce, a California Republican, called on Attorney General Jeff Sessions and Secretary of State Rex Tillerson "to hold individuals accountable" for the attack.
Turkey's embassy blamed the violence on groups linked to the Kurdistan Workers' Party (PKK) - a group fighting the government.
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While speaking about violence, Jaitley said that those people who resort to violence will be taken into account for their activities.
"This isn't Turkey. This isn't a third-world country", McCain said on MSNBC.