"I am the mayor. I made the mistake," Kilpatrick told Detroit residents, looking into the camera. "I am accountable."
A prosecutor is investigating whether the mayor and chief of staff Christine Beatty lied under oath during a whistle-blower's lawsuit last summer in which both denied having a physical relationship. A conviction of lying under oath can bring up to 15 years' imprisonment.
The mayor closed by saying, "God bless you, Detroit. I love you. I will see you at work tomorrow."
"I am angry, hurt and disappointed," she said. "But no question I love my husband."
The messages call into question testimony Kilpatrick and Beatty gave in a lawsuit filed by two police officers who alleged they were fired for investigating claims that the mayor used his security unit to cover up extramarital affairs.
Beatty submitted a letter of resignation Monday, effective Feb. 8.
"I feel he should go to jail for lying on the stand. He's embarrassing for everyone," said Joann Jackson, 63, who carried a white T-shirt bearing a depiction of Kilpatrick's face and the words: "JUST QUIT."