The Turkish Embassy meanwhile laid the blame on protestors "aggressively provoking Turkish-American citizens who had peacefully assembled to greet the president".
USA officials have criticized the Turkish government over violence outside its ambassador's residence in Washington.
Turkey called Thursday for the removal of the U.S. diplomat coordinating the global coalition fighting the Islamic State group in Iraq and Syria, accusing him of backing Syrian Kurdish militias.
The diplomatic incident has sparked outrage in Washington and even prompted the State Department to summon the Turkish ambassador.
News reported on Wednesday that the men who attacked the protesters were bodyguards of Turkish President Recep Tayyip Erdogan.
Senator calls for ejection of Turkish ambassador
The aide said two members of Erdogan's security detail were detained on the scene Tuesday by diplomatic security agents. McCain says, "We should throw their ambassador the hell out of the United States of America ".
The U.S. detained and released two members of the Turkish president's delegation after they were involved in an attack on peaceful protesters outside the Turkish embassy Tuesday.
"We told them ... we do not regard your cooperation with a terrorist group in Raqqa as healthy", Erdogan was cited as saying, but he said he expected a role for Turkey in Syria. A man with a bullhorn is repeatedly kicked in the face.
Last week, the Trump administration announced that it would arm the YPG - as a delegation of high-level Turkish military and intelligence officials were visiting Washington in advance of Erdogan's meeting with Trump.
In the footage which emerged yesterday, Mr Erdogan can be seen stepping out of a auto and watching on from a distance as his security personnel allegedly attacked Kurdish and Armenian protesters outside the ambassador of Turkey's residence in the U.S. capital. Nine people were sent to the hospital; two were arrested. Erdogan's security staff moved in to break up an anti-government protest after police refused to make the demonstrators leave a park across the street.
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 already telling you in advance, our rules of engagement give us this authority, we will take such a step and we won't discuss it or consult with anyone".
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Last night, Barcelona fans around the globe, had their fingers crossed that Celta Vigo could do us a huge favour. Bale may have to watch the Champions League final from the subs bench in his hometown.
A student waves a Turkish flag with a portrait of modern Turkey's founder Mustafa Kemal Ataturk during a march in support of the republic and against terrorism in Ankara on May 18, 2017.
Turkey's leader and his security team are guests in the United States.
The Trump Administration hasn't responded to the demand for an ouster, but McGurk's position appears in-line with the rest of the administration on arming the Kurdish YPG and using them against ISIS.
"We respect those concerns, and continue regular consultations with our North Atlantic Treaty Organisation ally on this and other topics of mutual importance", Nauert said.
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Democrats and Trump's fellow Republicans widely praised the appointment of a special counsel to take over the Russian Federation probe.