"There should not have been any physical contact in this incident," McKinney said in brief remarks on the House floor. "I am sorry that this misunderstanding happened at all and I regret its escalation and I apologize."
McKinney's comments came after the case had been referred to a federal grand jury for possible prosecution.
She had previously insisted she had done nothing wrong, and accused police of "racial profiling." She is African-American and the police officer is white.
McKinney, 51, has a history of confrontations with officers.
In this case, she entered a House office building without passing through the metal detector that screens visitors. Members of Congress are permitted to bypass the machines, but she was not wearing the pin that identified her as a House member at the time.
The officer, whose name has not been made public, has said he asked McKinney three times to stop. She did not.
Terrance Gainer, outgoing chief of the Capitol police force, has said that the officer placed a hand on her and she responded by hitting him. He said McKinney's race was not a factor.
The incident has embarrassed Democrats, including fellow members of the Congressional Black Caucus, none of whom have publicly defended her behavior in the March 29 incident.
It was not clear which, if any, of her colleagues had urged McKinney to make the statement she did.