"We commend the efforts of Mayor Bowser, Chief Newsham and all the law enforcement agencies involved in taking this step toward bringing the perpetrators to justice, and look forward to continuing to work with the relevant authorities to identify all involved", said ANCA Exective Director Aram Hamparian.
Two men were arrested at the time, and the US State Department registered concern to Turkey in the "strongest possible terms".
At least 11 people and one police officer were injured during the fighting. He is now awaiting extradition in New Jersey.
Twelve of the remaining suspects are Turkish citizens and have not been detained.
"I condemn this attack", Bowser said, adding the city will "defend the First Amendment".
The attack was an embarrassment for USA authorities, who invited Erdogan to meet Trump despite concerns over his government's increasingly authoritarian clampdown on his domestic media and opposition.
This after two Turkish men were arrested earlier Wednesday in connection to the incident, and charged with aggravated assault.
Newsham did not say how the police hoped to arrest the 12, saying the State Department would determine how to execute the warrants.
Narin and Yildirim were both participants in the protests, a US official familiar with the case told The Associated Press. Eleven people, including a police officer, were hurt in the brawl.
Turkish Ambassador Serdar Kılıç was summoned to the State Department the week after the brawl, a senior State Department official told CNN.
-Turkish ties. Relations were severely strained even before the May 16 clash, which happened as President Recep Tayyip Erdogan arrived at the Turkish ambassador's residence in Washington after a White House meeting with President Donald Trump.
Newsham said video showed security guards and some Erdogan supporters attacking a small group of protesters. A video posted online showed men in dark suits chasing anti-government protesters and punching and kicking them as police struggled to intervene. In another, they kick a different protester lying on the ground with a bullhorn.