The Turkish president was caught on camera observing the violence yesterday.
The protest turned violent, and nine people were injured.
In their Oval Office meetings Tuesday, Trump did not mention Erdogan's increasingly tight grip on power in Turkey or allegations of irregular elections under his leadership.
According to the video, one of Erdogan's bodyguard speaks with him while protesters chant slogans saying, "baby killer Erdogan".
In a statement, the Turkish embassy blamed the fighting on demonstrators who "began aggressively provoking" Turkish-American citizens who had assembled to greet Erdogan.
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The U.S. State Department has also expressed its official concern "in the strongest possible terms". They were assaulting these people on U.S. soil.
The altercation came the same day that Erdogan met with President Donald Trump at the White House.
The State Department condemned the attack Wednesday, and police in the nation's capital said they were working to identify the assailants, some of whom were armed.
"I ask that you immediately look into this matter and bring all appropriate criminal charges before these individuals leave the United States", Royce wrote.
The State Department summoned Turkish Ambassador Serdar Kilic following violence between Turkish President Recep Tayyip Erdogan's guards and protesters in Washington, D.C., this week.
"This kind of thing cannot go unresponded to diplomatically", he said, adding that legal action could be pursued.
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Metropolitan Police Chief Peter Newsham told a news conference Wednesday, "We intend to assure that there is accountability for anyone involved in this assault".
"I'd throw the Turkish ambassador out", the Arizona Republican told MSNBC's "Morning Joe", the Hill reported.
The YPG is the Syrian branch of the Turkish Kurdish Workers Party, the PKK, a Marxist group that has been trying since 1984 to carve out a separatist state from Turkey.
Turkey, the United States and European Union consider the PKK a terrorist organization.
The U.S. State Department said the episode was "deeply disturbing" and promised that an investigation would hold those responsible to account. "It's disgraceful and shouldn't be happening in the United States of America".
The Turkish Embassy also released a statement regarding the violence on Thursday.
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