The United States also revoked the visas of multiple guards, some of whom have not been charged.
Secretary of State Rex W. Tillerson said the charges should “send a clear message that the United States does not tolerate individuals who use intimidation and violence to stifle freedom of speech and legitimate political expression.” He said the department was still determining what, if any, additional steps would be taken.
The security personnel had been a part of Mr. Erdogan’s traveling protection detail during a visit to the United States last month.
On May 16, after Mr. Erdogan received a warm welcome at the White House, videos show those armed guards and other supporters attacked a group of protesters gathered outside the Turkish ambassador’s residence here. In another video, Mr. Erdogan can be seen watching the attack play out from a Mercedes-Benz sedan parked a few yards away. His role in the clash, if any, is unclear.
The standoff, which comes after weeks of careful maneuvering by the State Department over the case, complicates an already fraught relationship between Washington and Ankara.
Though allies and fellow NATO members, Turkey and America have grown distant in recent years because of American support for Syrian Kurdish forces that Turkey regards as a franchise of the P.K.K., a Kurdish nationalist militia fighting a guerrilla war in southeastern Turkey.
America is currently supplying arms to the Syrian Kurds to help them capture Raqqa, the capital of the Islamic State. Turkey fears these weapons will eventually end up in the hands of the P.K.K. in Turkey.
Mr. Erdogan is likewise frustrated by American reluctance to give up Fethullah Gulen, a Turkish cleric living in the United States that the Erdogan government accuses of masterminding last year’s coup attempt in Turkey.
Relations are also strained by the trial in New York of Reza Zarrab, a Turkish-Iranian associate of Mr. Erdogan’s, who stands accused of helping Turkey circumvent American sanctions on Iran.
Speaking during a dinner at his palace in Ankara late Thursday, Mr. Erdogan said the protesters had been a part of the P.K.K. and faulted the American officers for not controlling them.
“Can you imagine what would the attitude be if something similar happens in Turkey?” he said.
Some of the protesters were holding the flag of a Syrian Kurdish militia, which Mr. Erdogan and his government say shows them to be supporters of P.K.K.
The Foreign Ministry officials delivered a similar message in their meeting with the ambassador, saying that American law enforcement officials had not taken appropriate precautions to protect their delegation.
They said the police’s tolerance of “so-called protesters” near the ambassador’s residence ran “counter to any understanding of justice.”
And, as they had in an earlier summons with the ambassador, they accused the United States of not disciplining two American officers who they say briefly detained two Turkish security officers hours after the May 16 brawl.
In Washington, where lawmakers and advocacy groups have been pushing the American authorities to pursue charges, the reaction was altogether different as the news was greeted with calls for the State Department to go further in pushing Ankara to extradite the men.
After Thursday’s reaction, that does not appear likely. The men will be unable to re-enter the United States but likely cannot be prosecuted. If they were to return to the country, they would face a variety of felony and misdemeanor assault charges.
“I would like to be an optimist and hope that the people responsible for these things we all saw on video will come here and turn themselves in,” said Chief Peter Newsham of the Washington police.
Chief Newsham said that no staff members from the Turkish Embassy in Washington were implicated in the attack. He said that there were, however, several additional suspects whom law enforcement officials had not yet been able to identify and charge.
The skirmish in May does not appear to have been an isolated incident. In 2011, Mr. Erdogan’s guards took part in a fight at the United Nations that sent at least one security officer to the hospital.
And in 2016, the police and members of Mr. Erdogan’s security team clashed with demonstrators outside the Brookings Institution in Washington.