Turkey’s president denounced what he called the “scandalous” American judicial system on Friday, responding to new indictments of his bodyguards over a brawl during his visit to Washington in May.

The remarks in Istanbul by the president, Recep Tayyip Erdogan, underscored his view of the indictments as another affront in an increasingly strained relationship with the United States, a NATO ally.

Members of Mr. Erdogan’s armed security detail were captured on video punching, kicking and choking pro-Kurdish protesters, including American citizens, outside the Turkish ambassador’s residence in Washington on May 16. Video clips also showed that Mr. Erdogan, who was in Washington to meet with President Trump, witnessed the brawl.

Washington police officers intervened to halt the fighting, which the Metropolitan Police chief, Peter Newsham, described as a brutal attack on peaceful protesters that had left at least 11 people injured. American lawmakers and other officials expressed outrage that Mr. Erdogan’s guards had behaved in such a manner.