The clash Tuesday began when Erdogan's motorcade pulled up in front of the Turkish ambassador's residence, returning from a visit to the White House and a meeting with President Donald Trump.
Erdogan, emerging from his limousine, stood and watched as his guards and supporters began punching and kicking their way through a group of mostly Kurdish protesters across the street. Eleven people were injured.
Two senators protest
Two U.S. senators protested to Erdogan Thursday about his guards' behavior.
"The violent response of your security detail to peaceful protesters is wholly unacceptable," Senators Dianne Feinstein and John McCain said in a letter to Erdogan. They added that the incident was "unfortunately reflective of your government's treatment of the press, ethnic minority groups and political opponents."
U.S. Senators John McCain and Dianne Feinstein wrote a letter to the Turkish government, demanding it take responsibility for a clash involving protesters and President Recep Tayyip Erdogan';s guards near the Turkish Embassy in Washington on Tuesday.
While some Turks also decried the use of force to quash a peaceful protest, calling it a blemish on the country's international reputation and a violation of free speech, those who support Erdogan's increasingly authoritarian rule felt it was justified.
Protesters 'deserved to be beaten'
"Those terrorists deserved to be beaten," Atakan, a taxi driver from the city of Erzurum, told a VOA reporter. "They should not be protesting our president. They got what they asked for."
Yusuf Kanli, a newspaper columnist and political analyst, said no matter how bad it may have looked, the scene played right into Erdogan's image.
Watch: Anti-Erdogan Protesters Say They Were Attacked by President's Bodyguards
Anti-Erdogan Protesters Say They Were Attacked by President';s Bodyguards
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"I believe Erdogan makes use of this type of brawl for internal politics, to solidify his electorate and to get more nationalists to move to his party," Kanli said. "If you are an anti-Erdogan citizen in Turkey, you think like the civilized world and do not approve of beating people who think different from you. But if you are a pro-Erdogan citizen, you applaud when people who don't think like you do get beaten up."
Erdogan has bolstered his power base, particularly since a coup attempt last year. He has cracked down hard on dissent, jailing journalists and the leaders and other legislators of the PKK, a Kurdish party that was the second-largest opposition group in Parliament, on allegations of terrorism.
Growing political divide
The result has been a growing political divide in the country, as shown by results of a referendum last month in which voters narrowly approved even more sweeping powers for Erdogan.
"People who support Erdogan approve a show of force," Orkan, an engineer from Istanbul, told VOA. "So at the end, the sharp polarization within the country deepens more."
A similar clash between Erdogan's men and protesters broke out a year ago when he visited Washington for a nuclear conference.
"Turkish people who support Erdogan's AK Party see this sort of incident as legitimate," said Ilhan Tanir, a freelance Turkish journalist and analyst. "Pro-government newspapers and columnists are proof of that. They say they had to teach the PKK terrorists a necessary lesson.
"Erdogan's bodyguards remind me of Moammar Gadhafi's bodyguards," Tanir said. "They liked to get into fights, too. But with Erdogan's guards, violence has almost become a habit."