The United States said it voiced its "strongest possible" concern to Turkey over a street brawl that erupted between protesters and Turkish security personnel during President Recep Tayyip Erdogan's visit to Washington.

Police said the fighting outside the Turkish ambassador's residence on Tuesday injured 11 people, including a Washington police officer, and led to two arrests for assault. At least one of those arrested was a protester.

"We are communicating our concern to the Turkish government in the strongest possible terms," State Department spokeswoman Heather Nauert said in a statement on Wednesday.

A video posted online showed men in dark suits chasing anti-government protesters and punching and kicking them as police intervened. Two men were bloodied from head wounds as bystanders assisted dazed protesters.

Metropolitan Police Chief Peter Newsham said in a news conference on Wednesday that police had a good idea of most of the assailants' identities and were investigating with the Secret Service and State Department.

Turkey's official Anadolu state news agency reported that protesters were chanting anti-Erdogan slogans as the president entered the residence after meeting US President Donald Trump to discuss the fight against Islamic State of Iraq and the Levant (ISIL, also known as ISIS) fighters.

"Police did not heed Turkish demands to intervene," the news agency said, and Erdogan's security team and Turkish citizens moved in and "dispersed them".

The Turkish Embassy did not respond to a request for comment.

Tens of thousands of Turks have been detained as Erdogan cracked down on the press and academia following an attempted coup in 2016.

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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.

In a statement, Washington Mayor Muriel Bowser called the violence "an affront to DC [District of Columbia] values and our rights as Americans".

Mehmet Tankan, 31, said he was one of a dozen protesters outside the ambassador's residence chanting slogans when the brawl broke out.

"The next time they could kill us easily. I'm scared now too because I don't know how it will affect my life here in the United States," said Tankan, who lives in Arlington, Virginia.