"We are communicating our concern to the Turkish government in the strongest possible terms", State Department spokeswoman Heather Nauert said.
Footage filmed by VOA Turkish showed men, many wearing dark suits, hitting and kicking protestors, including some lying on the ground, while police officers tried to prevent the assaults.
Erdogan was in the US capital on Tuesday to meet with President Donald Trump.
Officials alleged in the statement that the protesters were affiliated with the separatist Kurdistan Workers' Party, or PKK, which is designated a terrorist organization by Turkey and the United States.
Police said they were in "the preliminary stages" of an investigation into the incident.
"We clearly told them if there is any attack by the YPG against Turkey, we will apply the rules of engagement without asking anyone", he was quoted as saying by the Hurriyet newspaper Thursday.
Erdogan's visit on Tuesday was further complicated by Turkey's calls for the United States to take steps to extradite Turkish cleric Fethullah Gulen, who has lived in self-imposed exile in Pennsylvania.
It's not clear to what extent President Erdogan's full security team was involved. Dozens of Kurdish-Americans rallied outside the Turkish ambassador's residence in DC to protest Erdogan's crackdown on dissent, with more than 130,000 people detained. Two arrests have been made in connection to the attack, according to the Washington Free Beacon.
Erdogan said Tuesday that cooperation between the US and Turkey is "very important for the world" and vowed to expand economic and military ties between the two countries.
But that account differs greatly from the sequence of events described by protesters and video captured by the Voice of America Turkish service they said was taken at the scene.
Erdogan's party did not immediately respond to the allegations, but pro-government and state-run media in Turkey blamed the incident on supporters of the PKK and YPG Kurdish armed movements.
Eleven people, including a U.S. police officer, were hurt in the fight.
In a statement, Peter Newsham, police chief for the District of Columbia, complained of a "brutal attack on peaceful protesters".
"My Kurdish friends and allies were protesting peacefully against Erdogan being in Washington when we were suddenly attacked by a group of Erdogan's official bodyguards and secret police", Ceren Borazan wrote on Facebook.
At their meeting Tuesday, Trump said the USA would re-establish its military and economic partnership with Turkey, committing to backing Turkey's defense against both Islamic State and the PKK.
Anadolu, Turkey's national news agency, reported that protesters chanted slogans against Erdogan as he entered the ambassador's home after meeting with US President Donald Trump in which they discussed the battle against ISIS fighters.
Republican Senator John McCain also censured the "thuggish behavior". "Because we have no time to lose", he said.