The NATO allies are still at odds over a USA decision to arm Syrian Kurdish rebels fighting the Islamic State group in Syria.
The new warrants come after four other pro-Erdoğan protesters were arrested over the past month, and a congressional resolution condemning the attacks.
New Jersey contractor Eyup Yildirim - seen in video footage attacking protestors with Erdogan's bodyguards and kicking a woman - was charged with assault with significant bodily injury and aggravated assault.
Warrants were also issued for two Canadian citizens, he said.
The department released no further details about the suspects but said additional information would be available Wednesday.
Nine protesters were injured in what D.C. Mayor Muriel Bowser described during a news conference Thursday as a "vicious attack". Turkey is also a key USA ally in its campaign against Islamic State militants, but the two nations have butted heads over their respective relationships with Kurdish fighters, some of whom the US has armed even though Turkey claims the groups are terrorist organizations.
The men, all Turkish citizens, include nine Erdogan security guards and three Turkish police.
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.
Turkey's Foreign Ministry has called in the United States ambassador to Ankara, John Bass, for talks after USA authorities issued arrest warrants for a dozen official Turkish security guards involved in a brawl with protesters in Washington last month. The Turkish Foreign Ministry then summoned America's ambassador to address about the treatment of the detained security guards.
"We will fight politically and judicially" against the warrants, Erdogan said in a speech in Ankara, accusing Washington DC police of allowing "terrorists" to demonstrate against him when he visited the White House last month.
The Turkish embassy claims the bodyguards were acting in self-defense, accusing the protesters of being affiliated with a Turkish opposition group.
It is highly unlikely that Turkey would extradite the men to the United States to face the charges, but they do face the possibility of arrest should they ever try to re-enter the country.