Two U.S. citizens are already under arrest for their part in the attack, and the District of Columbia now seems certain to request the extradition of Ellialti and Dereci on felony charges. The MPD, State Department and U.S. Attorney's Office teamed up on the investigation.
Mahmut Sami Ellialti and Ahmet Cengizham Dereci face charges of felony assault with significant bodily injury. Department spokeswoman Heather Nauert declined to say what actions might be taken, but the US could seek the extradition of the Turkish suspects or bar them from entering the United States.
Mr Newsham said: "We all saw the violence that was perpetrated against the protesters".
Warrants were also issued for two Canadians and two Americans.
Authorities said they identified the suspects by comparing video of the melee to passport and visa images, using facial recognition techniques.
A still shot from footage of the clashes between Turkish security forces and protesters last month.
The security officers are no longer protected by the immunity extended to them during Erdogan's recent visit, the State Department said. "We support them to make sure they are safe".
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A total of 18 arrest warrants have now been issued over the brawl, which left nine people in the hospital after the fight escalated outside of the Turkish ambassador's D.C. residence.
"They should bring themselves here to the United States to answer these charges", Newsham said.
United States prosecutors have charged a dozen Turkish security personnel after an attack on protesters during President Recep Tayyip Erdogan's visit to Washington, prompting an angry denunciation by Turkey's leader.
Whether or not the Turkish citizens, who were all either Turkish security officers or Turkish police officers, will ever actually face charges in the USA remains to be seen.
Turkish officials have admitted that security officers participated in the fracas but said they were acting in self defense, contending that protesters started the brawl and that D.C. police refused to arrest them. Men in dark suits and others were recorded repeatedly kicking one woman as she lay curled on a sidewalk.
The Turkish embassy claims the bodyguards were acting in self-defense, accusing the protesters of being affiliated with a Turkish opposition group.
Video of the startling violence, widely circulated on social media, showed security guards pummeling a group of protesters with fists and feet.
The incident comes amid increasingly strained tensions between the US and Turkey, a North Atlantic Treaty Organisation ally that has grown more authoritarian in recent years under Erdoğan's leadership and drawn criticism from prominent USA politicians.
The incident has certainly raised tensions with Turkey, and American officials may continue to be disappointed with their attacks on protesters.