Worthy had been looking into claims that Kilpatrick and one-time Chief of Staff Christine Beatty lied under oath during a whistle-blowers’ trial last summer when they denied having a romantic relationship in 2002 and 2003.
The Detroit Free Press in January reported excerpts of text messages on Beatty’s city-issued pager that contradict their testimony.
A perjury conviction for lying under oath could bring up to 15 years’ imprisonment and may force Kilpatrick to relinquish his hold on the mayor’s office.
On Tuesday, the Detroit City Council approved a nonbinding resolution asking Kilpatrick to resign.
The mayor repeatedly has said he won’t step down and says he is pushing on with city audits, budget and other business issues.
"I’m more focused now than I’ve ever been in this job," Kilpatrick told reporters following Tuesday’s council vote. "I think I’ve grown up a lot in this process, and I think we’re moving forward."
Kilpatrick also said he will continue to work with the council despite the resolution.
Some council members have "reached out" by voicemail on continuing to work together on city business, he said.
In response to the numerous criminal charges, the mayor has denied any wrongdoing and said he would not resign.
Attorneys for the mayor and Beatty said on Monday that their clients would be exonerated.