Its resolution laid the blame at the door of bodyguards working for Turkey's President Recep Tayyip Erdogan, saying they had beaten up Kurdish protesters.
The Turkish embassy previously said the demonstrators had aggressively provoked Turkish-Americans gathering to greet the president, who was visiting the US.
Eleven people were injured.
Videos of the incident appear to show Turkish security officials punching and kicking unarmed Kurdish demonstrators.
"Any Turkish security officials who directed, oversaw, or participated in efforts by Turkish security forces to illegally suppress peaceful protests... should be charged and prosecuted under United States law," the resolution states.
Turkey has demanded a full investigation.
House speaker Paul Ryan urged the Turkish government in Ankara to "finally accept responsibility for this egregious incident and apologise to those who were harmed".
The Congress has called for criminal charges against those involved in a brawl outside the Turkish ambassador's residence in Washington DC last month.